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DEGREE OF DIFFICULTY

 

by Valentino Piana (2007)

     
 

Contents


 
 
1. Significance
 
 
2. Determinants
 
 
3. Impact on other variables
 
 
4. The relevance for consumer theory
 
 
5. The relevance for firm theory
 
  6. The relevance for the labour market  
 
7. Difficulty vs. risk
 
 
8. How to formalise difficulty
 
 
9. Empirical scales of degree of difficulty
 
 
10. Formal models
 
 
11. Data
 
 
 
 

Significance

Something difficult is neither easy nor impossible. It requires skills, effort, attention, but still the result is not guaranteed.

"Difficulty" is a key concept for a new economics, because mainstream neoclassical economics distiguishes only what feasible from what impossible, without allowing this intermediate category so relevant in reality.

People face difficult tasks, thus have to cope with them by learning, technology, social networking, etc. To a large extent, the fact that acquiring information, elaborating it, delivering a proposal that matches conflicting criteria are all difficult tasks constitutes the rationale for bounded rationality and its simplifying routines.

In neoclassical perspective, everything can be bought. Difficulty would be reduced to the cost of overwhelming it. But difficulty cannot be overwhelmed by purchase: money does not make a normal person understanding high mathematics, whatever the effort.

You need innate talent, skills, a peculiar personal history; to acquire skills you need priceless time in non-outsourcable exercise and there is no guarantee that you will succeed: you may spend you life in trying to jump higher than the world champion but never achieve this.

In certain situations, certain people can have a pleasure in drilling and learning more and more difficult things. However most of the people most of the time prefer to take it easy, being also more sure of the result.

Not only individuals face difficult tasks; also firms encounter difficulties in management, they can fail to achieve their objectives and to implement their choices.

In another vein, there is an important relation between difficulty and motivation. A slightly more difficult task than the present skill level would guarantee is particularly motivating: too easy or impossible tasks are less motivating that challenging tasks.

Determinants

A task is difficult because of its in-built structure. In certain cases, the difficulty is imbedded in one key component of what has to be performed. However a rising number of difficult components makes the overall task more and more difficult.

Difficulty would be particularly high when the task is complex and cannot be performed by solving successively several elementary components.

By comparing the in-built structure with the skills of the people trying to perform, one can say that a difficult task requires high, specific, and rare skills.

As a general analogy, you may think at what happens in climbing mountains. Indeed, there is a recognised system of classification of the degreed of difficulty of a mountain path, based on many factors such as the the kind of the rock, the degree of vertical inclination, the length, the presence or absence of natural aids, etc.

For more intellectual tasks, take the example of memory. Words that are easy to remember remain short and well connected to others, whereas difficult ones have long and unusual pattern.

"A-A" is easier to remember than "assatmani", while "afsdfindlfasdfinklkdfafpollibnlknkfadfsdffs" might be impossible if you are not given enough time and incentives and you do not device some method / technique / technology.

More in general, a proper technology can sometimes help in overwhelming difficulty. The lack of it makes the task difficult or impossible. Thus innovation should be understood as the attempt of overcoming difficulties.

In some cases, what's important is the level of skill in a vertical scale (low, medium, high,...). In this cases, you may expect learning being important in improving the skills of the potential user, from early childhood context to broad and narrowed-focused teaching. Repetition of the task, imitation of good performace (maybe under rallenty) and explanations for failures might help.

In other cases, what matters is the presence of a specialised skill: a Chinese ideogram is difficult to remember and reproduce to almost everybody, but not to a Chinese person (an example of horizontal differentiation of skills).

In still other cases, skills are useless. Let's imagine that in an experiment you are asked to remember what they show you for a short while. A square is easy to remember, an irregular shape cannot be reproduced exactly, independently from whom you are.

Impact on other variables

The degree of difficulty influences the rate of failure, the good quality of the result, the speed of the execution. When difficulty is high, there is a high rate of failure, the result tends to be poor and the execution lengthy.

The degree of difficulty impacts the time and the cost of learning, with long period with highly skilled teachers being required if difficulty is high.

However you are not granted that you can overcome the difficulty by paying only: you need to engage yourself, make use of your general and idiosyncratic skills, have some luck. All this in larger amounts the more difficult the task.

As a consequence, the number of people / organisations / agents able to perform that task depends on the degree of difficulty. High difficulty is associated to a low number of successful agents.

The relevance for the consumer theory

There are four main areas of consumer theory that are influenced by the notion of "difficulty":

1. The elaboration of information used to choose the good to buy

2. The technical difficulty to use the good as an additional constraint to the choice

3. The non-exhaustion of budget as a prudential rule

4. The choice at prices near the reserve prices

5. Preference building processes.

Sub 1. Experiments with real consumers have shown widespread difficulties in memorising prices, brands, and features of goods. This means that comparisons among potential substitutes are usually limited to what is exposed in the current point of sale, with some simple heuristics used to postpone purchase if strongly disappointed by its supply.

People tend to remember just few brands for each category of goods (e.g. biscuits or toothpaste), with a large group of consumers trusting only those brands, so that new entrants have a strong barrier to overcome.

The comparison of goods with respect to their features is difficult, so attention is concentrated on one (or few) most important features (lexicographic rule) or avoided through sequential choice (one version is tested against certain minimal thresholds in a set of features; if it passes the test it is bought without looking for another; if it does not pass the test a further version is tested, and so on) or coped with through other heuristics, as in this model of ours.

When the consumer does compare different versions, then it may be faced with a truly "difficult choice" if each version has defects and unpleasant sides.

Sub 2. If a good is technically or socially difficult to use as well as it requires a high level of specialised expertise, many consumer would renounce to buy it, even if they need it and would like to buy it. The distribution of the skills of the consumer (and socially acceptable behaviours) becomes a further constraint to the diffusion of goods, especially of innovative ones.

This also implies important inertia and lock-in phenomena against superior but non-standard solutions in favour of older products (as in the famous case of Dvorak and QWERTY keyboards for writing machines).

In other words, the utility that neoclassical theory attributes to goods is in the real world dependent on actions taken which make use of those goods, with the skills of the performer being an important determinant of the final outcome. The performer is commonly the consumer himself, but can well be a third person (be paid or not), so the too-simple mapping of preferences over a Cartesian space of good quantities (indifference curves) is too weak to grasp significant features of real-world decision-making.

Sub 3. Contrary to timeless neoclassical theory of consumer choice, the consumer takes decisions over time (real days, real weeks, real months,...). He never exhausts the budget, as the neoclassical consumer does by choosing a bundle on the budget line, because he wants to keep room for further purchases, planned and unplanned.

If an expenditure is planned, small, corresponding to highly valued needs, it will be easily carried out. If abruptly a large expenditure proposal arise, which is clearly unnecessary, maybe even in contrast to other's opinion, the consumer will have difficulties in making up his mind. He may be tempted to postpone the choice.

Sub 4. In many cases, the consumer a priori decides a maximum price he is willing to pay for satisfying a certain need. This price is called his "reserve price".

This, often implicit, practice can be easily introduced in formal models of consumer behaviour, as this. If the price of the good is near the reserve price, the modeller might use - to forecast purchasing - a probability distribution of purchasing instead of the deterministic rule of 100% purchase below the reserve price and 0% of probabilty of purchase above it that we used in the first version of this model.

Sub 5. People prefer goods and services presented at and exhibiting the "proper" level of difficulties. Newbies prefer easy things, masters prefer difficult things. Little babies tend their arm towards things in front of their eyes and easy to grasp; later on, they notice new things passing by quickly and hidden, rotating their heads and discarding what they have in front to get what they noticed. From difficulty degree to preference: this is a new insight in consumer theory, as we abandon the neoclassical assumption of preferences as "given" (from where? by whom? through which process?). It's because a good has the "right" level of difficulty that it appeal to the consumer.

The relevance for the firm theory

Production is difficult. It requires a vast array of technical and non-technical competences which are difficult to acquire, coordinate, maintain, improve. These competences are embedded in organizational routines performed by real people making use of material and immaterial assets, capital goods, territorial landscape, social networks. These resources are not necessarily for sale; this limits the number of firms operating in a market because entrants may not own the "know-how" to properly produce. Their money may not be sufficient for "purchasing" skills because some skills are simply not on the market.

It's true that they can try to imitate the incumbents, but imitation is usually difficult, i.e. costly, long, and with no guarantee of success. Entrants can try to leverage their own knowledge base in other sectors and make an effort in Research & Development in order to innovate current practices, but again R&D is difficult and not available to everyone.

Imagine that you would like to enter the market of craftmade pottery; you need training but you still have no guarantee that you will succeed. Imagine the difficulty for a new unexperienced firm to build a dam. Who would give it the permission to experiment, putting at risk people in the valley?

Contrary to the neoclassical approach based on isoquants, productive tasks do not neatly fit into the dychotomous categories of "feasible" and "not-feasible": they are "difficult"!

In other words, the competence-based theory of the firm, whose importance is rising in the battlefield of ideas, clearly assumes that production is difficult and that only firms with a sound competence can carry out it. Accordingly, maintaining and nurturing core competences and strategically complementary competences become keys to business success.

Given this assumption, industries can be judged in reference to the digree of difficulty they present. If production is comparatively easy, the competences needed might be owned by a fairly large number of firms (or to acquire them may be relatively easy for new entrants). Without other barriers, the industry will probably comprehend many small firms, especially if there are not many possibilities for "best performers" to differentiate from the rest. On the contrary, if production is highly difficult (e.g. it requires a widely differentiated body of formal and non-formal knowledge), then just few firms could put together the necessary skills.

Industrial concentration thus can be traced back, among other factors, to the degree of difficulty in production, innovation, imitation.

In another vein, if several firms have different skills to produce a difficult product, their supply will be vertically differentiated, with highly skilled firms producing better versions of the product.

The relevance for the labour market

High difficulty is associated to a low number of successful agents. This has important consequences for wages: jobplaces with easy tasks, requiring very broadly available skills, are usually paid less than jobplaces with difficult tasks, where only few can succeed. The latter have a higher bargaining power with respect to the firm. All this is true irrespective of the profits the overall combination of tasks leads to products sold on the market.

Indeed, contrary to the neoclassical theory of wages being determined by marginal productivity of the individual worker, it is usually impossible to discern the contribution of each worker to the final product, because the outcome depends on team-work and coordination, and even less so to profits (which are determined by much more than just physical productivity).

Since difficulty is an important determinant of wages, the workers have an interest in increasing the difficulty of the tasks (and to increase and differentiate their skills), whereas the firms prefer innovations that homogenize tasks and labourforce. This tension impact the technological trajectories, backed by R&D and product innnovation.

Difficulty vs. risk

"Difficulty" should not be confused with "risk", although both have to do with probabilities. Something can be risky but not difficult: gambling is risky but require no skills (it's exactly because non-skilled person can earn a lot of money by betting that roulette gambling is so appealing to them). Conversely, a master can manage even difficult tasks without any risk of failing.

How to formalise difficulty

Evolutionary economics presents many formalised agent-based models in the form of computer simulation. Essentially, a simulation is computer code embracing several algorithms. Each algorithm has a role, as for instance to determine whether a firm obtains an innovation or not.

When a role requires the expression of a certain degree of difficulty, five basic elements should be in place:

1. a level of skill;

2. a success level;

3. an "effort" component, usually costly (sometimes coupled with an "attention" component, usually free but scarce);

4. a first random draw to determine whether success is reached or not.

5. a second random draw, contingent on success, to determine the quality of the result.

If the degree of difficulty is very low for everybody, the success level is very low and the random draw would exhibit a large probability of success, even for low level of effort. If the degree of difficulty is low for skilled-enough agents, then the success level is very near to the level of their skill.

Coherently with these settings of low difficulty, the second random draw would lead to good quality results with high probability.

On the other extreme, to express an overall high livel of difficulty, the level of success is set very high, with probability zero to be reached from low levels of skill and with requiring high level of effort even from more skilled agents to get a significant probability of success. In the (unguarantee) case of success, the quality of the results again might have a distribution of probability skewed to the left, with most random draws falling at low level of quality.

Formalising difficulty in this way allows, however, many intermediate and mixed cases. In particular, it allows for skills to be important or not.

In case of success, it is possible (but not necessary) a feedback on the level of skill (learning). An independent algorithm for learning (e.g. with imitation or explicity taking "lessons" from a teacher) might be also in place.

This algorith can be extended to cover more of our earlier discussion. In particular, a number of horizontally differentiated skills could be introduced (e.g. the foreign languages known by the worker).

More in general, any routine of bounded rational agents is somehow an answer to the difficulty of the task.

Empirical scales of degree of difficulty

In practice, there exist categorial scales of difficulty based on the skill level requested to address them. A simple scale distinguishes three levels: Beginner, Intermediate, Advanced.

Tasks characterised by these levels can be described with the following keywords:

Beginner - quick, easy, little to no experience, basic, straight, very little equipment requested;

Intermediate - some very basic skills, very basic understanding of technical terms, challenging to someone with no experience;

Advanced - for people with good grasp of the subject, experienced, good supply of equipment, a fair understanding of how to use this equipment.

A more refined scale would include sub-levels, such as:

B1, B2, B3,

I1, I2, I3,

A1, A2, A3.

More complex schemes for attributing the difficulty to what has been performed can be exemplified by this paper on synchronized skating.

Formal models

The production function of students' degrees where it is difficult ot get good marks

A model of dynamic competition where goods are difficult to use and R&D is difficult

Data

The NASA classification of R&D activities according to the degree of difficulty

The degree of difficulty in a sport discipline: synchronized skating

 

 
 
 
 
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