Math Formula

Tuesday, November 20, 2012

And Why Did You Go To Bosnia At All?

Ironically, even though I have spent two years in BiH now already, I haven't thought about covering that frequently asked question here on this blog. However, recently I ran into this very nice blog post from Snježana about foreigners in ex-Yugoslavia, so it crossed my mind to share my story as well.
In the light of Scott Hanselman, I will give the gift of my keystrokes not only to her, but to all of you.

So why did I go to Bosnia at all?
Some background about myself and my family first. My father's parents were "Danube Swabians" (Donauschwaben) who lived in Slavonia, in a small village some 40km from Osijek. Even though some of them did speak some Serbo-Croatian, their main language was some obscure dialect of German (with quite an undeniable Croatian influence). Also, culturally they rather perceived themselves and were perceived as "Germans in Slavonia".
By the end of the WW II, they had to escape from the partisans, and landed in Upper Austria.

As much as I was aware of that fact, it didn't really play a role in my childhood in the 90's. I had a rough picture were my ancestors had originated from, but I grew up as an Austrian child with Austrian dialect and Austrian habits. Also, I wasn't particularly interested into where exactly they had lived, how they had lived, and how they had ended up in Austria at all. Yet, in the very back of my mind some connection remained.

Studying in Vienna, I started working for a company which does business in Europe and beyond. For various reasons, I was quite open to the idea of working and living abroad as well.

First, that's what job advisors keep telling you - whatever you do, gain some experience abroad first! I think I never really understood the reason behind, and rather took it for some fancy bla-bla - until I realized that it does make a difference (which I will not go into now, though, but maybe in some "Bosnia-aftermath" which it is too early for now).

Second, I was fond of travelling even before; so why not extend the journey and stay somewhere even longer, say, two years? Obviously, the perspective that you get and the experience you gain is way more than on a typical weeks to month trip. Getting to know habits, language, people ...

Third, of course this was a great work opportunity as well. Taking responsibility for a big project and making nice money always comes handy.

So, yes, I was ready to go abroad. But why exactly Bosnia, then?

Well, simply because it happened. There arose this opportunity for this project in BiH, at a moment I was ready for it.
Thus, I cannot claim that living in BiH is what I have always dreamed of - but when the opportunity arose, I was more than ready to take it (or maybe the opportunity arose exactly because I was ready for it?), and I haven't regretted it a single moment.

Wednesday, November 14, 2012

Dreadful Crimes - At All Times?

"Dreadful crimes? But I can assure you that crimes just as dreadful, and probably more horrible, have occurred before our times, and at all times, and not only here in Russia, but everywhere else as well. And in my opinion it is not at all likely that such murders will cease to occur for a very long time to come. The only difference is that in former times there was less publicity, while now everyone talks and writes freely about such things--which fact gives the impression that such crimes have only now sprung into existence."

Who knows me a little bit (or follows this blog and therefore knows why I try to avoid news) might realize that this sounds quite a bit like me.

However, this is a quote from Fyodor Dostoyevsky's "The Idiot", written in 1869.

150 years later, I cannot help being surprised about how accurate this is even today.

It makes me wonder, once again: Apart from us driving cars, exchanging messages within seconds online and eating Big Macs, what has substantially changed for society as a whole in the meantime?

Wednesday, October 17, 2012

The Tragedy Of Public Spending In Six Sentences

Political leaders are supposed to give precise spending forecasts, even when the details of the projects to be approached are not yet known.

If a project budget is not fully used up, the politician is said to be a poor forecaster, and less money than actually needed will be allocated to her future projects. Thus, a project budget is always fully used.

If the forecasts are exceeded, the politician is said to be a poor forecaster as well, plus he has to struggle to get the additional funds needed. Thus, there is an incentive to make the initial forecast bigger than actually expected.

As there is no incentive to counter these increased costs, always more money is spent than actually needed.

Monday, October 15, 2012

Updated Blog Style

After more than a year of writing this blog and a extremely lame layout and overall look & feel, I felt it was about time to make a small redesign and several improvments for things that always bothered me.

First of all, you will note a new theme - instead of the blue font on what background you will now find a combination of dark colors (black, grey) and orange.

Next, I tried to get rid all the unnecessary clutter on the page - label overview, archive, about me section are all now cut away from the main page. Instead, I created dedicated pages for archive and a quite rudimentary "about" page as well.

Furthermore, I found that I did not offer any possibilites to get in touch with me - so here they are!

Finally, I moved to feed burner for feed generation, which also allows subscribing via email now.

And what do you, dear reader, think about the new design? Each kind of feedback is truly welcome!

Tuesday, October 2, 2012

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

In last week's post, I discussed the question of a whether a free good should always be consumed, or if it might make sense to abstain from consumption under certain circumstances.

We went through four examples of consumption.
In example 1 and 2, the saturation factor was low (\(s = 0.2\)).
In example 1, the consumer always consumed, and gross utility \(g = 26\).
In example 2, the consumer abstained in period 2, and gross utility \(g = 20\).

In example 3 and 4, the saturation factor was high (\(s = 0.6\)).
In example 3, the consumer always consumed, and gross utility \(g = 18\).
In example 4, the consumer abstained in period 2, and gross utility \(g = 20\).

So, here is the answer to our initial question: You should eat or not eat the apple depending on the saturation factor \(s\) ! For a big \(s\) , not consuming in period 2 was better; for a small \(s\), consuming was better.

However, at which threshold does the decision change?

Let's make a step back first. As you might have noticed, I only varied the decision for period 2, and here's why.

In period 1, consuming is always superior to not consuming. There was no prior period from which the consumer might still be saturated, so he always consumes. Thus, we can assume \(c_1 = 1\), and can disregard the consumption decision from now on.

As we have seen, changing the decision in period 2 has an effect on the gross utility, so \(c_2\) remains a variable to be considered.

However, period 3 can be disregarded again. Why? If \(c_2\) was 0, there is no saturation, and similar to period 1, consumption is better. If \(c_3\) was 1, there is saturation, but there is no 4th period to save consumption for, so again, consumption is better. Thus, \(c_3 = 1\) , and can be disregarded further on.
The only variable to maximize against is \(c_2\).

In the light of the above, let's reconsider our gross utility function:
\(c_1 = 1\)
\(c_2 =\) to be seen
\(c_3 = 1\)
\(u_1 = a c_1  = a\)
\(u_2 = a c_2 (1 - c_1 s) = a c_2 (1 - s)\)
\(u_3 = a c_3 (1 - c_2 s) = a (1 - c_2) s) = a - a c_2 s\)

\(g = u_1 + u_2 + u_3 = a + a _2 (1 - s) +  a - a c_2 s = \)
\(2 a + a c_2 - a c_2 s - a _2 s = \)
\(2 a + a _2 - 2 a _2 s = 2 a + a _2 (1 - 2s)\)

Now we can directly compare the two outcomes with each other; the gross utility in case of consumption in period 2 (which is , and the gross utility in case of no consumption in period 2.

So, for \(c_2 = 1, g\) would be: \(2 a + a (1 - 2s)\)
And for \(c_2 = 0, g\) would be: \(2 a + 0 = 2a\)

So, this question can be formulated as inequation:


\(2 a + a (1 - 2s) > 2 a\)
\(a (1 - 2s) > 0\)
\(1 - 2s > 0\)
\(1 > 2 s\)
\(1/2 > s\)
\(s < 1/2\)


So, if the saturation factor \(s < 1/2\), gross utility is bigger with \(c_2 = 1\).
For \(s > 1/2\), gross utility is bigger with \(c_2 = 0\).
For \(s = 1/2\), the consumer is indifferent, so the gross utility is equal.

Conclusion
Of course, your real saturation factor \(s\) is hardly known. However, I find it quite interesting to keep in mind that for a big saturation factor, I should rather consider not consuming. The bigger the impact on the reduction of the satisfaction of tomorrow's consumption, the more I should be inclined to defer consumption.

Critique
As I mentioned above, I'm well aware of the fact that this model is still very weak.

First of all, the approach of trying to quantify utility of consumption, especially of non-tangible goods might be quite inappropriate. After all, that's the major weakness of the homo economicus altogher, right?
As a defense, I'd like to see the approach chosen not as a purely numerical, but rather as a concept as whole. You can imagine and include whatever you want into this utility function.

Second, the assumptions and constraints are very restrictive. Consequently, the results might not only be inaccurate, but even wrong and misleading.
The assumptions should incrementally be loosened in further research. I intent to do so in upcoming weeks.

Third, some empirical studies should be conducted, until the theory can eventually be rejected (Karl Popper again).

I hope that I managed to make my point, and am looking forward to all kind of additional critique and feedback.

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?


Assumptions
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).

Analysis
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 \(s = 0.6\).
\(c_1 = 1\)
\(c_2 = 1\)
\(c_3 = 1\)

so:

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

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.


Update:
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!

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