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.

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.

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) 10 8 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) 10 0 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) 10 4 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) 10 0 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

Neophobiac Or Neophiliac ... And What Are You?

"If I had asked people what they wanted, they would have said faster horses." -- Henry Ford (despite the questionableness of this quote)

As some of you might have heard already, the upcoming incarnation of Microsoft Windows will offer a completely new user experience called Metro. It is expected to look roughly like this:

Source: microsoft.com

Apparently, they are trying to create the same experience on all devices in the future - be it a desktop PC, a tablet, or a smartphone. As for all things newly invented or changed, the press, current and potential users, bloggers, ... are pretty divided into two groups: 

• The ones defending what is today, opposing change, willing to stick to what they've come to know over the past decade.
• And then there are the others, who are outright nuts for the new style, ignoring it's potential glitches and shortcomings

In psychology, two technical terms are used to describe the two extremes of the spectrum:

• Neophobia is "the fear of new things or experiences", on the contrary to 
• Neophilia, which describes a person with strong affinity to novelty.

However, a person is not always purely the one or the other, but might be rather neophile regarding certain questions (for example, enjoying the new immediately iPhone once it's released), and rather neophobe regarding other (for example, denying that humans are descendants of apes). Also, one's attitude towards novelty is most likely to change over time. Who might have been wildly seeking for change and revolution in early years might take exactly the opposite stand once he's older (and in some rare cases, vice versa).

I'm quite convinced that each society and organization needs both types. People who drive innovation and change on the one hand, but at the same time, others who do not follow them blindly, but see to some reality check every now and then and throttle the craziest ideas.

All in all, this makes me wonder, which stand you should take? Should you promote change and new ideas? After all, you will not be able to stop change anyways ... like it or not, your children will not even know what this VHS was back then, so better get rid of it now and start adopting new things accordingly!

Or should you rather wait and see what happens, for many new ideas and technologies are doomed to disappear after a couple of years anyways, so why adopt at all? Something in between? If so, when and under which circumstances?

As you see, dear reader, I cannot come to any conclusion on this (maybe there is none). So for me, the question remains, neophobiac or neophiliac ... and what are you?

About The Freedom Of Goods

Chapter 2 of "TITLE I - Free movement of goods" of the Consolidated version of the Treaty establishing the European Community provides the basis for one of the four major pillars of what is referred to as the Single Market.

According to europa.eu,

... controls on the movement of goods within the internal market have been abolished and the European Union is now a single territory without internal frontiers.
The abolition of customs tariffs promotes intra-Community trade, which accounts for a large part of the total imports and exports of the Member States.
Articles 28 and 29 of the Treaty establishing the European Community prohibit import and export restrictions between all Member States. However, if there is a threat to public health or the environment, Member States may restrict the free movement of goods.

This renders the EU a customs union, a special type of free trade area. Well, good and nice - as long as you find yourself on the lucky side of globalization, and as long as you don't happen to live in a country which is implicitly excluded from the union, by not being explicitly included. Like, say, Bosnia for example, in which case even purchasing a kindle via Amazon can become quite lengthy a process.

I will not dive into the pros and cons of free trade vs. protectionism now (oh, just found there is an entire article dedicated to the free trade debate on Wikipedia). Instead, I want to tell you how surprised I was again this week.

As some of you might remember, I bought a motorbike a while ago. Since I found that registering a vehicle can be quite complex a task for a foreigner in Bosnia (and, I assume, in most other countries too), this bike is now registered on a local friend's name. Recently, I talked to two Austrian custom experts, about me driving to Austria with 'my' BiH bike. Bang! Shake-heads, absolutely no, how can I even think about it (that's the young, naive European again), no way!

Just to be clear: Even with a written permission from the owner, I (as a citizen of an EU member state) must not 'import' any vehicle from a third-country ... and in that context, simply driving the vehicle across the border, and be it just for one hour, is 'importing' already.

I must confess, this requires me to rethink the entire idea of 'importing'. For me, that was rather permanent a thing, i.e., with the intent of using something for an extended period, or selling it. On the contrary, the liability to declare a good already arises by simply moving the good across the border, disregarding intended duration and purpose.

But, you might think, what happens if my friend rides the bike across the border, and I just use it afterwards? Well, I was informed, that's "abusive usage" then, representing a criminal act from both of us ...

Thinking the other way round, the same is true if I lend my Austrian car to a friend here - "abusive usage"! I'm neither a lawyer nor a customs expert (however I'm guilty of istism right now), and I guess there is some rationale behind that interpretation (am I also guilty of being naive now?), but my common sense simply cannot see anything wrong about it. It is my friends bike, and he is lending it to me, so why should I not drive to Austria, or any other place I want to?

I don't know whether the EU in general is too positively perceived at the moment, but giving me the freedom to lend my stuff to whomever I want, for whichever purpose I want, is clearly a great thing ... and that is what the Freedom of Goods is all about.