UC Davis UC Davis Previously Published Works Title A simple model of technological intensification Permalink https://escholarship.org/uc/item/5tk1r0k0 Journal Journal of Archaeological Science, 33(4) ISSN 0305-4403 Authors Bettinger, RL Winterhalder, B McElreath, R Publication Date 2006 DOI 10.1016/j.jas.2005.09.009 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Journal of Archaeological Science 33 (2006) 538e545 http://www.elsevier.com/locate/jas A simple model of technological intensification Robert L. Bettinger*, Bruce Winterhalder, Richard McElreath Department of Anthropology, One Shields Avenue, University of California at Davis, Davis, CA 95616, USA Received 12 July 2005; received in revised form 15 September 2005; accepted 19 September 2005 Abstract Ugan, Bright and Rogers [When is technology worth the trouble? Journal of Archaeological Science 30 (10) (2003) 1315e1329] develop procurement and processing versions of an optimization model, termed the tech investment model, to formalize the conditions that favor invest- ing time in the manufacture of more productive but more costly technologies. Their approach captures the tradeoffs that occur as less costly versions are supplanted by more costly versions of the same category of technology (e.g., fishhooks), but not the tradeoffs that occur when more costly categories of technology supplant different but less costly categories used for the same purpose (e.g., hook and line vs. spear). We (i) propose an alternative model in which different categories of technology are characterized by separate costebenefit curves, (ii) develop point-estimate and curve-estimate versions on this model, and (iii) show how they might be applied using the development of weaponry in ab- original California as an example. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Technology; Technological investment; Bow; Atlatl; Human behavioral ecology; Foraging theory; Marginal analysis 1. Introduction problems of this kind. We argue that while the UBR techno- logical investment model represents intensification within Ugan, Bright and Rogers [9] develop procurement and pro- a given technological category, it misrepresents what happens cessing versions of an optimization model, termed the tech in- when one category (e.g., hooks) replaces another (e.g., spears). vestment model, showing that as increased time is devoted to We recommend the use of alternative approaches we believe these subsistence activities it pays to invest more in technolo- are more generalized as well as easy to implement. In the in- gies that increase their rate of return. Theirs is an important terest of space, we attend here only to the procurement version conceptual contribution, formalizing intuitive insights found of the UBR model. in archaeological and ethnographic discussions of technologi- cal change. We see analytical problems, however, in the way 2. Conceptual problems with the UBR model Ugan, Bright and Rogers (hereafter, UBR) operationalize the model, specifically in their illustration of how technological The key relationship in the UBR procurement model is both functions are derived, which is said to be their primary goal simple and familiar: increasing investment in technology im- [9, pp. 1318, 1323]. Granting theirs was a mainly heuristic ex- proves procurement returns at a decreasing marginal rate, as ercise and that, as they note [9, pp. 1317, 1318] they were where harvesting a resource requires a tool that when crudely forced to take liberties with their empirical data, we worry made in 1 h produces a net gain of 1 kg/h, and when more finely that others will follow their methodology when exploring made in 2 h produces a net gain of 1.5 kg/h. Here, the first hour of technological investment increases the rate of procure- ment by 1.0 kg/h, the second hour by only 0.5 kg/h. Since the * Corresponding author. Tel.: C1 530 752 0551; fax: C1 530 752 8885. crude tool generates a higher rate of procurement per unit of E-mail address: [email protected] (R.L. Bettinger). technological investment, the more costly form will make 0305-4403/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jas.2005.09.009 R.L. Bettinger et al. / Journal of Archaeological Science 33 (2006) 538e545 539 sense only in the presence of other factors, the most salient be- several possible candidates for the specific form of this func- ing the amount of time the tool is used for procuring resources. tion, they prefer the negative exponential: We call this variable its use time, designated by u. If return ÿ Á Z ÿkm rates for a particular technology are imagined as being maxi- f ðmÞ a 1 ÿ e mized relative to use time in addition to the time spent in man- ufacture, more costly technologies can outperform less costly where ones. In the example above, if exactly 1 h is spent in resource f ðmÞ is the rate of return, procurement, the crude and finely finished tools will produce a is the maximal possible rate of return, exactly the same overall rate of return: made in 1 h and used k is the rapidity with which the function reaches its maxi- for 1 h, the crude tool yields 1 kg, or 1 kg/2 h Z 0.5 kg/h; mum value, and made in 2 h and used for 1 h, the finely finished tool yields m is the time invested in the technology. 1.5 kg, or 1.5 kg/3 h Z 0.5 kg/h. The critical use time, y, for the finely finished tool e the amount of time that must be de- They plot the manufacturing times and return rates of each voted to procurement to make it viable in the presence of its technological alternative for Great Basin fishing and compute cruder counterpart e is thus 1 h. If any more than 1 h is spent a best fit for the negative exponential to the set of points. From in procurement, the more costly technology generates the this curve they determine the critical procurement times re- higher rate of return; if any less than 1 h is spent in procure- quired to make each technology viable relative to the next ment, the cheaper technology is preferable. In our terminology, least costly alternative. ya4b represents the critical use time for switching from tech- The results are intuitively plausible: large procurement use nological alternative a to b or back. time is required to justify costly technologies (Table 1). By UBR [9, pp. 1317e1320] illustrate this principle using their calculations, while it takes only about 0.04 h of fishing Great Basin fishing data [5,8] that document the return rates time to justify the 2.25 h needed to fashion a simple hook associated with different categories of technology used for La- and line, it takes more than 9155 h to justify the 350 h needed hontan cutthroat trout (Oncorhynchus clarki henshawi) and to make a 100# gill net [9, Table 2]. cui-ui (Chasmistes cujus): hook and line, spear, multiple We believe, however, that the UBR approach is inappropri- hook, A-frame dip net, and 100# gill net, from least to most ate in this context because the technological improvements costly (see our Table 1). They envision the general form of that increase Great Basin fishing returns are not appropriately the relationship between return rate and alternative forms of represented by a single, continuous function, the alternative technological investment in Great Basin fishing gear as a con- technologies (hook, spear, net) not being continuous develop- tinuous function that increases at decreasing rate, the tangent ments of each other. A spear is not a modified hook, any more to which at any given point defines the critical use time (y), than a net is a modified spear. Because they are discretely dif- i.e., procurement time required to justify the corresponding ferent kinds of things, hook, spear, and net are more properly amount of technological investment [9, their Fig. 1].Of characterized by separate functions. When so conceived, mar- ginal analysis of intensification over alternative categories of Table 1 technology and the calculation of critical use time times re- Critical use times, yx4y, for fishing technologies under the point-estimate and quired to justify a particular investment are easy to compute UBR [9] models and, importantly, often different than that found by UBR [9]. Technology Return Manufacturing fi(mi)/mi Critical procurement As they note [9, p. 1317], UBR conceive their model as a a b rate fi(mi) time mi time yx4y analogous to Charnov’s [1] marginal value theorem and to (kg/h) (h) Point-estimate UBR [9] Metcalfe and Barlow’s [6] model of field processing and trans- (h) (h) port. However, in both these models, a single, continuous Hook and line 3.413 2.25 1.52 0.00c 0.04 function is used to represent only one patch- or resource- Spear 34.483 4.00 8.62 ÿ2.06d 0.11 type; in fact, having a unique, continuous curve defines the Multiple hook 103.093 30.50 3.38 9.32 7.54 type. Alternative patches or resources require a multi-curve A-frame dip net 200.000 99.00 2.02 42.37 115.13 version of the model [cf. 7], not the alignment of multiple # 100 gill net 250.000 350.00 0.71 905.00 9155.45 patch- or resource-types along a single curve. At several points a Data from Ugan et al. [9, Table 1]. during their discussion UBR [9] invoke broadly similar cases: b Computed for each technology relative to its next least costly alternative, $5000 professional stoves and $300 chef’s knives vs. a mone- e.g., spear vs.