Throughout the medieval period right up to the Protestant Reformation, there was attempted entry in parts of the areas dominated by the Western church. Heresies abounded in many areas—Gnosticism and Walden-sian heresies, dissenters emerging within the structure of Christian religion (Savonarola), and heresies arising from an emerging scientific state of mind were all present. The Church responded vigorously to attempted entry with policies ranging from outright war (the Crusades), to inquisitions that long preceded the emergence of Protestantism, to other forms of religious sanctions such as excommunication and interdict.67 Indeed, the emergence of religious orders such as the Franciscans and the Dominicans were aimed at addressing the entry possibilities of those advocating a more "Christ-like" church that ministered to the poor and sick. Generally, then, the Church engaged in a policy of raising entry costs to would-be entrants. Heresy—as defined by the Church— could be paid for with one's life. But there was another economic strategy available to the Church in forestalling or preventing entry—limit pricing.
Limit pricing is defined as follows: ''A firm is limit pricing if it sets its price and output so that there is not enough demand left for another firm to enter the market profitably.''68 The key to limit pricing is that the incumbent firm must convince potential entrants that it will produce the same output (e.g., Qi in figure 8A.1) regardless of entry. Assuming the market is being served by the incumbent at an existing price, p0, the new firm will face residual demand curve, DR, upon entry. The incumbent firm must convince the entrant that in will ''overproduce'' if necessary to drive down the price to a point that denies profit to the entrant (i.e., p1, where the entrant's residual demand curve is tangent to industry average cost, AC). However, this course is not very plausible because
Cathedral construction as a form of limit pricing according to the incumbent's demand curve, DM, price pi yields average revenue below average cost. Therefore the outcome depends on the credibility of the incumbent firm in making such a threat. With a credible threat the incumbent can reap monopoly rents in the interim. The usual channels used by the incumbent firm to signal its commitment are huge physical plants and long-term contracts. However, if entry occurs, the entrant will prove that the incumbent cannot sustain the output Qi, and thus price will not fall by much, making the entry profitable and presumably encouraging more entry.
We suggest that an economic reason that the Catholic Church built huge cathedrals was to signal to potential entrants its commitment to maintaining market share or even increasing it. In addition to many functional by-products (guild meeting halls, and so on) they created, cathedrals were also signaling devices of brand name capital as described by Benjamin Klein and Keith Leffler.69 The import of the signal was to indicate to prospective entrants (Protestants and others) that excess capacity existed for Roman Catholic religion and membership. (The corporate headquarters of large corporations—such as the Transamerica building in San Francisco—may provide evidence that the business is here to stay, for example.) In this way, firms, including the Roman Catholic Church, invest in brand name capital to create a "grandeur effect.'' Unquestionably, this strategy worked for a long period of time prior to the Protestant entry. The pre-Protestant heretics were unsuccessful despite the fact that there were repeated attempts at entry right up to the Reformation. But Protestant entry proved that in certain locales entry into the religious market was profitable, a fact that encouraged more entry.
Protestant entry can be seen in part as a result of the failure of rational policies to prevent entry. At some point someone was going to test the hypothesis of profitable entry and find it viable. In the interim, the Church was behaving rationally in deterring entry by investing in excess capacity. According to a model of limit entry pricing, the Catholic Church failed to convince the potential entrant (Luther) that it could sustain Qi. Why did such a policy fail to convince potential entrants at the time that it did? It may be that the monopoly Roman Catholic Church had become so large and locationally diverse that is was unable to effec tively monitor the signaling of all of its agents. But the theory of limit pricing, outlined above, suggests that the leader of entry at this time estimated that the Catholic signals were unenforceable and that it was an economically plausible policy to call the Church's bluff. Additionally, he was willing to accept the potential personal costs (death).
Entry was not a surprise to the Church, and it most certainly did not willingly allow Protestants to enter the Christian religious market. Rather the Church exhibited rational expectations, investing less in excess capacity in areas where entry was likely to succeed in spite of its efforts. It was too costly to fight entry in particular locations, so the incumbent firm chose to retreat from those locations and concentrate on others. Note that our argument is unaffected by the fact that the great period of cathedral building originated in the twelfth century; actual construction took place more or less continuously for centuries (see table 8A.1), and it helped deter entry from a number of heretical forms. Other entry-limiting devices were of course used by the Church, including repression and murder. Hundreds of thousands of people were tried, condemned, relieved of property, or killed. Witchcraft, in addition to more formal heresies, was severely condemned, with thousands murdered between 1300 and 1499 alone.70
Ours is a signaling theory, whereby actions taken are not taken for the sake of their direct results, but to inform prospective rivals or competitors. Fund raising and work on cathedrals was part of the entry deterrence strategy. We hypothesize that in the face of entry, the Catholic Church found it less costly to give up some locations to the Protestants than to fight. The testable implication here is that the pattern of investment in cathedrals reflects the Church's expectations in this regard. Our model also conjectures that once a successful entry occurs, more entry is encouraged; this is definitely the case today in the United States, where the religious market is becoming a competitive world in which everyone can follow the religion they want.
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