Overhead labour and bounded substitutability
SummaryIn this paper we argue that due to the presence of quasi-fixed overhead labour, the aggregate short-run production function of the industry has the property of bounded substitutability. That is, when employing overhead labour, the industry will only be able to earn a positive quasi-rent for a bounded interval of aggregate labour intensity.
The distribution approach to the aggregation of production functions
We shall argue below that the distribution approach to the aggregation of production functions provides an useful framework to analyse the production structure of an economy and enhances our understanding of it. The distribution approach was initiated by Houthakker (1956), elaborated by Johansen (1972) and extented by Sato (1975). Apart from summarising the main features of the distribution approach developed by these authors in a consistent framework, we also add new insights. Some of these insights stem from our earlier research, e.g. the interpretation of the aggregate short-run production function and the estimation of the capacity distribution. However, the extension of the analysis to economy-wide aggregation has not been presented before. The same holds for the role capital plays according to the distribution approach in both the short-run and in the long-run production function.An important feature of the distribution approach is that the production structure of an economy is seen as the result of both management decisions and technological possibilities. Moreover, the approach enables us to identify production units and their production functions at any desired micro level. As a consequence, the influence of technological change on the production structure can be analysed extensively. The same holds for changes in output prices and factor prices, through their influence on management decisions.
Strategy and Manipulation in Medieval Elections
There are many goals in developing electoral protocols, including a desire for a system which is transparent, in that it is clear what the rule or procedure to follow is; nonmanipulable, in that it is not in a person’s best interest to misrepresent their preferences; honest, in the sense that it elects the ‘right’ candidate; and not open to strategizing, i.e., bribery or collusion. However, these desiderata are in tension with each other: Often, transparent electoral procedures are the least strategy resistant, and many honest procedures encourage manipulation. Thus a balance between these different goals must be sought. In modern times, since the seminal result on vote manipulation, the Gibbard-Satterthwaite Theorem [5, 6], much attention has been devoted to developing voting rules where manipulation is never in the best interest of the voters [4] or which are computationally too complex for the average bounded agent to be able to manipulate [1]. This focus on computational aspects of electoral methods is one of the hallmarks of modern studies on voting. But pursuit of these goals is not restricted to modern times: Those participating in elections in the Middle Ages also sought transparency, non-manipulability, honesty, and strategyproofness in so far as these properties can be consistently expressed in a single procedure. However, given the lack of computational sophistication in the Middle Ages, alternate approaches were needed in order to promote honesty, discourage strategizing, etc. These approaches can be classified as either external (constraints introduced outside of the electoral procedure, such as incentives for coming to consensus quickly) or internal (constraints introduced within the electoral procedure, such as voting rules which cannot be manipulated without adverse effects, or which are too difficult for the average bounded agent to manipulate). Surveying examples of both approaches in the context of medieval ecclesiastical and secular elections provides an interesting comparison to modern electoral procedures. Elections in the Middle Ages were used for the same reasons that they are today: To select suitable candidate(s) for a particular office, duty, or obligation. However, it is important to note that the term electio was used in the Middle Ages in a broader sense than our modern ‘election’. Its primary sense was ‘selection’ or ‘choice’, and only secondarily ‘election’ in the modern sense. Thus, many records which purportedly discuss elections are not discussing elections of the type which interests us. We can identify four categories of medieval electoral processes: (1) Election by an external authority having no direct interest in the election; (2) Indirect election, where electors name other electors who then select or elect the officials; (3) Election by lot; and (4) Election by ballot. Elections of the first and third types are generally computationally uninteresting; the first type corresponds to dictatorial voting rules, and the third type collapses to probability theory. In general, interesting voting methods are found only in the fourth type, election by ballot, though they can also occur in indirect election.