Total Endowment Research Articles

“Students find corporate reforms absurd”: Bryn Mawr Student’s Mobilization for Divestment from Apartheid South Africa

In 1986, Bryn Mawr College’s endowment held $8 million or 8.33% of its $96 million endowment in investments tied to Apartheid in South Africa. In line with other major US institutions who believed they must act moral in the face of violent and exploitative system of racial discrimination, the Board of Trustees, the governing body that oversees college operations and finances, proposed a plan in 1985 to divest from subsidiaries of their stock in South Africa if Apartheid was still in place 24 months later in 1987. This came at the tail end of the international movement to oppose and end Apartheid through economic pressures. Bryn Mawr students would reject this plan, occupying buildings and mobilizing campus to disrupt Board meetings. Students said they would not rest until full divestment. Their movement held a shared commitment to ending Apartheid in South Africa and to ending racism in the United States. This paper narrates how the social and economic movements against Apartheid panned out at Bryn Mawr College in the 1980s. Based on my original primary source research at Bryn Mawr and Haverford Colleges’ special collections, I uncover the tactics and frameworks of the student movement to divest as well as the college’s response. Inevitably, the administration took partial measures to accommodate some of the demands of the student movement for divestment. The nexus between the student movement for divestment and the college administration took new heights in 1986. In this year, the students rejected the college’s newly presented plan for divestment, as they understood it as a mere palliative measure in the face of the violence and racism of Apartheid. To understand the student zeitgeist at the time , I illuminate the historical context of the movement against Apartheid by situating it in relation to the preceding anti-War and Civil Rights movements. The later era of activism precipitated into the New Left movement, which was a radical student movement grounded in ideas of political and economic democracy. I provide readers with a primer on the foundations of ethical investment in South Africa. The college’s plan embodied the corporate responsibility ethos of the 80s, which sought to maintain capitalism and pacify very popular alternatives through modest reforms. These principles undergirded Bryn Mawr College’s eventual divestment strategy, which sought to maintain profit and to make a statement about their opposition to the political system of Apartheid. To make this argument, I draw on archival discussions of corporate responsibility politics and the theory of change they espouse which forwarded reform through pressuring the companies they held stock in. I engage in an analysis of discourses emerging from a school-sponsored trip to South Africa in the winter of 1986, which was dubbed a “Peace Mission Fact Finding Trip.” This analysis is essential to understanding student and faculty perspectives, as there was not a consensus on the subject. In the end, Bryn Mawr adopted a divestment plan that was in the name of corporate responsibility. They wrote letters to the corporations they held stock in who had subsidiaries in South Africa, and asked what they were going to do to end Apartheid. The school sold $651,558 in 1986 of stock from the 5 companies, a mere 0.67% of the total endowment.

The implementation of the Italian National Seismic Prevention Plan: A focus on the seismic upgrading of critical buildings

The Italian National Seismic Prevention Plan (NSPP) was issued following the destructive 2009 L'Aquila earthquake, with a total endowment of 965 million euros granted by law, under the coordination of the Italian Civil Protection Department (ICPD). The NSPP addresses seismic risk reduction according to a broad view, through multi-task programs. Among the measures granted by NSPP, one is devoted to the seismic retrofit of strategic or critical public buildings and infrastructures, whose damage or collapse may affect emergency management as well as produce high consequences in terms of human lives.The paper provides a preliminary assessment of such seismic prevention measure, through some statistical elaborations on a sample of around 1000 interventions, 375 of which so far concluded. The analyses carried out on this sample provide interesting information to verify the effectiveness of the measure as well as to enhance further actions similarly purposed.Analyses on seismic risk indices of critical buildings included in the NSPP are presented and discussed in the paper, together with an early analysis of costs and benefits associated with different structural types, and intervention types. The results obtained highlight interesting aspects in terms of seismic safety increases and marginal costs for the masonry and reinforced concrete buildings of the considered sample. These preliminary results, though requiring further calibrations on the larger datasets foreseen in the future, provide useful hints to envisage how they could be used in the definition of future strategies for seismic risk reduction. To this aim, a final paragraph provides an exemplification and a simplified procedure based on the findings shown in the paper, for comparing costs and benefits of different strategies aimed at reducing the risk of a given portfolio of buildings.

Polyphase gold mineralization at the Yaou deposit, French Guiana

Abstract The Yaou deposit, located in French Guiana within the Guiana Shield, is one of the most promising gold deposits of the regional Paleoproterozoic greenstone belt. It displays numerous quartz monzodiorite bodies aligned along a sinistral shear zone where a five-deformation phases model is established at the camp scale. The ductile D 1/2YA phase is responsible for the main penetrative foliation while the D 3YA phase is related to shearing. An intrusive event is identified as being pre to syn-D 3YA . The following phase D 4YA represents a brittle quartz-carbonate veining set hosted preferentially within intrusive bodies and along the shear zone. A local D 5YA brecciation event crosscuts the D 4YA veins. Among this deformation history, two auriferous events (D 3YA and D 4YA ) control the overall grade of the Yaou gold deposit. More specifically, most of the Au grade is associated with the main economic D 4YA veining event, where the gold is visible and linked to Py 4 within an ankerite/hematite rich alteration halo. At the microscopic scale, results of in situ analyses using LA-ICP-MS on pyrite show that metasediment-hosted Py 0 is a primary source of submicroscopic gold having a low contribution to the total endowment. Py 3 shows some gold content due to possible remobilization of Au D0YA . Gold in Py 4 is found as submicroscopic gold, as micro-inclusions and as infilling fractures in association with elements such as Te, Ag and Bi. Most contribution to the Au grade is from micro-inclusions and, to a lesser extent, from free and submicroscopic gold. The ore shoot locations are lithologically controlled for Au D0YA (metasedimentary unit-hosted), structurally controlled (shear zone-hosted) for Au D3YA and rheologically controlled for the Au D4YA (intrusion-hosted). The deposit is clearly polyphase both at the macroscopic and the microscopic scales, invisible gold is associated with As whereas visible gold is observed as inclusions in pyrite with high contents of Ag, Te and Bi. We define an early low-grade enrichment of Au D0YA to Au D3YA followed by a later high-grade event, Au D4YA supporting polyphase mineralization processes. This study confirms that orogenic gold deposits can be formed by remobilization and/or new gold inputs during multiple deformation, veining and hydrothermal events.

Non-Separable Household Model (Household Production and Consumption Decisions in A Market Failure)

Households in developing countries are systematically exposed to market imperfections and shadow prices play a similar role to market prices in the decision process of the household. When they apply, the shadow prices are equal to marginal utility of the consumption of food and leisure, and marginal productivity of labor. They indicate the price that the household would be willing to pay to have the corresponding constraint relaxed by one unit. Hence, household characteristics in consumption, total time endowment, exogenous cash transfer ( ), and consumption prices affect production decisions as opposed to the separable household model. Transaction costs should be reduced by the Governmental and non-governmental institutions to narrow the gap between purchasing and selling prices, and increase market participation of households and also increases their gain from changes in price. Keywords: production and consumption decisions, market failures, shadow price, transaction costs, non-separable DOI: 10.7176/JMCR/78-02 Publication date: April 30 th 2021

Modelling gold potential in the Granites-Tanami Orogen, NT, Australia: A comparative study using continuous and data-driven techniques

The Granites-Tanami Orogen (GTO), a poorly exposed component of the North Australian Craton, is host to significant Paleoproterozoic orogenic gold mineralization amounting to a total endowment of greater 20 Moz Au. This study adopted a multi-technique approach to mineral potential modelling (MPM) of orogenic gold deposits in the GTO, using four different techniques: Continuous fuzzy gamma, geometric average and data-driven index overlay and data-driven random forest methods. The predictive models generated in this study delivered the first public-domain gold prospectivity maps for the Northern Territory (NT)-portion of the GTO. The predictor maps at the core of these models represent mappable proxies of mineralizing processes believed to have been critical in the formation of the orogenic gold deposits, and were generated in the framework of a mineral systems approach. Normalized density, prediction-area and area under the receiver operating characteristic curve methods were used to test the robustness of these predictors and determine the most effective. The performance of the gold potential models generated in this study was assessed using the improved prediction-area plot procedure, with the data-driven random forest approach having delivered the best performing model. The multi-technique approach taken in this study, in which multiple mineral potential models are generated for the same study area and using the same predictor maps, is a relatively new and, as of yet, underutilized approach to MPM that, in contrast to the standard procedure (i.e., generation of a single data- or knowledge-driven model) ensures optimal utilization of the available conceptual and empirical information, helps to better understand and minimize stochastic and systemic uncertainties, facilitates cross-validation of the resulting prospectivity models, and allows the resulting models to be compared and contrasted. From a practical, exploration point of view, the models served as decision-support tools that helped to improve confidence in targeting underexplored, gold-prospective areas in the GTO more effectively and identify new search areas previously not recognized as areas of high gold potential.

Predicting grade-tonnage characteristics of undiscovered mineralisation: application of the USGS Three-part Undiscovered Mineral Resource Assessment to the Sandstone Greenstone Belt of the Yilgarn Block, Western Australia

ABSTRACT The United States Geological Survey (USGS) Three-part Undiscovered Mineral Resource Assessment provides a framework for estimating undiscovered mineral endowment. Previous studies that applied the Three-part Assessment to estimate the undiscovered orogenic gold endowment of the Sandstone Greenstone Belt, Western Australia, have relied upon dated or expert-derived grade-tonnage models. Here, several assessments are conducted using local grade-tonnage models, comprising known orogenic gold deposits within the entire Yilgarn Block and several individual terranes with contrasting lithosphere- to terrane-scale characteristics. These models are generated through comprehensive review of historical exploration, resource and production data. Based on these models, the Sandstone Greenstone Belt is estimated to contain significant undiscovered gold mineralisation, with a median total endowment of between 166 and 298 t gold, and mean of 167–319 t gold. Although these updated grade-tonnage models provide an approximately 80 per cent variation in predicted gold endowment, it is still evident that the belt remains an under-explored region within the Yilgarn Block, Western Australia.

Assessing the variability of expert estimates in the USGS Three-part Undiscovered Mineral Resource Assessment methodology: A call for increased skill diversity and scenario-based training

Abstract Future mineral exploration will necessarily be conducted in increasingly challenging and uncertain search spaces as near-surface, high-quality ore deposits are progressively depleted. Faced with this increase in task complexity, an important consideration from an exploration management perspective is the behavioural aspect of information interpretation and decision-making. One such challenging search space is the Sandstone Greenstone Belt, Western Australia, covering an area of approximately 920 km2, that is deemed prospective for the discovery of archean orogenic gold deposits, with mined (historic production), inferred and indicated resources (JORC 2004 and 2012) totalling 54 t Au. Gold endowment estimates made by geoscience experts, during an exploration project evaluation workshop, were compared with estimates from a group of non-geoscientists, made during a separate but identical workshop. Significant differences were identified between the estimates of the expert geoscientists and the non-geoscience expert group, with the latter proving more conservative. However, a portion of the geoscience experts (N = 11) group produced conservative estimates, comparable to a non-geoscience expert group (N = 10), with both suggesting the existence of additional gold deposits of similar size and quality to known resources (with group estimates for median total endowment of 99 t and 120 t Au, respectively). The remaining geoscience experts (N = 11) presented significantly more optimistic, albeit inconsistent, estimates for the gold endowment of the project area, predicting the existence of undiscovered deposits significantly larger than those already defined in the belt (with a group estimate for median total endowment of 350 t Au). Although the true undiscovered gold endowment within the project area remains uncertain, several possible factors can explain the variations in estimates. These include the application of contrasting strategies, with participants opting to apply more empirical or conceptual methods, and to differences in background experience, resulting in distinct skillsets and varying ability to estimate uncertainty. To improve the quality of expert estimates, it is suggested that individual expertise and appropriate assessment strategies can be developed through scenario-based training courses, and that greater skill and experience diversity within exploration teams is desirable, leading to more balanced aggregate estimates. Further research is warranted to determine which, if any, of the proposed factors account for these disparities. This research could be used to adapt the composition of exploration teams and develop training programs to promote the development of expertise in predictive exploration targeting, in order to promote discovery of future mineral resources.

Efficient and strategy-proof allocation mechanisms in many-agent economies

In this paper, we show that in pure exchange economies, any Pareto-efficient and strategy-proof allocation mechanism is alternately dictatorial; that is, it always allocates the total endowment to a single agent even if the receivers vary. While many studies have shown that such an allocation mechanism is dictatorial in two-agent economies, it has long remained an open question whether such a characterization can be obtained in many-agent economies.

Litho-structural controls on orogenic gold deposits within the Sandstone greenstone belt, Yilgarn Craton, Western Australia: implications for exploration targeting

ABSTRACTThe 920 km2 Archean Sandstone greenstone belt lies in the central-northern part of the Southern Cross Domain of the Youanmi Terrane, Western Australia. The belt, forming an arrow-head geometry, is bounded by the Youanmi and Edale shear zones on its eastern and western margins, respectively. The belt has a total gold endowment, including historic production, resources and reserves, of approximately 62 t (2.0 Moz). Most known deposits are situated within a central-southern ultramafic domain, although this is likely a function of exploration focus. The distribution of historical exploration efforts and domaining of deposit types, based on litho-structural controls on ore formation, highlight the potential for significant undiscovered deposits, hosted within arrays of shear zones parallel and adjacent to the lithosphere-scale Youanmi and Edale shear zones.

Detrital zircon U–Pb ages of Paleo- to Neoproterozoic black shales of the Baikal-Patom Highlands in Siberia with implications to timing of metamorphism and gold mineralization

A U–Pb isotope system of detrital zircons was used to determine the provenance and maximum deposition age of the Paleoproterozoic Mikhailovka and the Ediacaran Khomolkho, Aunakit and Dogaldyn Formations in the Baikal-Patom Highlands, one of the most ancient components of the Central Asian Orogenic Belt (CAOB). The Baikal-Patom area hosts the world-class Lena orogenic gold province with total endowment of up to 6000 tons Au. The gold deposits are confined to the compressional syn- or post-metamorphic structures at various stratigraphic levels in Paleoproterozoic to Neoproterozoic black shale sequences deposited in the Bodaibo passive margin of the Siberian platform. Nine samples were collected from mineralized rocks to address possible detrital zircon recrystallization and transformation during superimposed metamorphic and hydrothermal events. Zircon was analyzed using laser ablation – single collector – magnetic sectorfield – inductively coupled plasma – mass spectrometry (LA-SF-ICP-MS).The Mikhailovka metasediments yielded three concordant isotopic age clusters: predominant Archean (2.45–3.25 Ga), Paleoproterozoic (1.96–2.10 Ga), and Cambrian-Ediacaran-Cryogenian (524–702 Ma), whereas most of the zircon grains yielded discordant isotopic ages. Multiple lines of evidence (i.e., grain morphologies, specific set of mineral inclusions, distinctly high U and Th in zircon, and several persistent Pb-loss arrays of discordant ages with lower intercepts of concordia line at closely the same point) suggest the youngest cluster combines formerly metamict zircon of different ancient ages recrystallized under the peak conditions of the regional metamorphic event synchronous with or slightly preceding mineralization. Therefore, the youngest detrital grain isotopic age of 1961 ± 20 Ma determines the maximum depositional age of the Mikhailovka sediments that predates the emplacement of the Paleoproterozoic collisional Chuya-Nechera granitoids.Zircon grains from these granitoids represent a major population in the overlying Ediacaran sequences that indicate the prevalence of supply from proximal local sources, such as the uplifts of the ancient Siberian basement within the Bodaibo paleobasin. The age span of the Neoproterozoic detrital zircon population (604–966 Ma) in the younger formations is in agreement with the events in the CAOB and Siberian platform.

Control of Shear-Zone-Induced Pressure Fluctuations on Gold Endowment: The Giant El Callao District, Guiana Shield, Venezuela

The El Callao district, with a total endowment of more than 2000 t Au, is considered to be the most prolific gold resource in Venezuela. Mineralization is hosted by a vein system that is genetically associated with the El Callao transpressional shear zone. This vein system consists of a network of interconnected quartz–albite–ankerite veins enveloping a large number of metabasaltic fragments that host gold-bearing pyrites. Based on detailed mineralogical, microstructural, and fluid inclusion studies, a pressure-temperature pathway was established for the evolution of the mineralizing fluid during shear-zone development and exhumation. This path is characterized by repeated episodes of fluid pressure fluctuation from lithostatic (higher than 1.6 kbar) to near-hydrostatic values (<0.4 kbar), recorded throughout the transition from the quasi-plastic to frictional deformation cortical domains. Each successive pressure drop induced boiling of the hydrothermal fluid, with the resulting fluid phase separation controlling: (i) pyrite and invisible gold crystallization, which occurred during ductile and ductile-brittle transition strain conditions, and (ii) primary gold remobilization with consequent native-refined gold precipitation, occurring mainly under brittle conditions. The metallogenic framework that was proposed for the El Callao shear zone can be used as a vector to explore and characterize other mineralized shear zones in the Guiana Shield and analogous orogenic systems worldwide.

Zircon U-Pb, molybdenite Re-Os and muscovite Ar-Ar geochronology of the Yashan W-Mo and Xiatongling W-Mo-Be deposits: Insights for the duration and cooling history of magmatism and mineralization in the Wugongshan district, Jiangxi, South China

To test the impact of cooling history and prolonged hydrothermal activity on the grade and total endowment of the tungsten deposits, we obtained new and detailed geochronology from the Yashan W-Mo and the Xiatongling W-Mo-Be deposits in the Wugongshan mining district in Jiangxi Province, South China. Both deposits contain stockwork and greisen ores within contact zones between granitic plutons and wall-rock metasandstone and mudstone and within the granitic plutons. New SHRIMP U–Pb zircon analyses yielded weighted mean 206Pb/238U ages of 231.0 ± 5.0 Ma and 161.5 ± 1.8 Ma for the monzogranite and granite in the Yashan W-Mo deposit, and 154.7 ± 1.7 Ma for the granite in the Xiatongling W-Mo-Be deposit. Three molybdenite samples from stockwork ores in the Yashan deposit and four molybdenite samples from greisen and stockwork ores in the Xiatongling W-Mo-Be deposit yielded Re–Os isochron ages of 156.0 ± 2.8 Ma and 156.4 ± 8.7 Ma, respectively. Two muscovite samples from greisen W-Mo ores and W-bearing stockwork in the Yashan deposit gave 40Ar/39Ar plateau ages of 152.77 ± 0.78 Ma and 152.36 ± 0.78 Ma, and two muscovite samples from greisen W-Mo-Be ores and W-Mo-bearing muscovite-quartz stockwork ores in the Xiatongling deposit gave 40Ar/39Ar plateau ages of 146.85 ± 0.8 Ma and 146.31 ± 0.75 Ma, respectively. The age data indicate that the ore-forming granitic magmas were emplaced earlier at the Yashan deposit than the Xiatongling deposit, but Mo mineralization was concurrent at both deposits, and the last hydrothermal ore-forming alteration started earlier again in the Yashan deposit.The U-Pb, Re-Os and Ar-Ar geochronological data indicate that both deposits had similar durations of magmatic-hydrothermal process: 9.1 ± 1.9 m.y. for the Yashan deposit and 8.6 ± 1.8 m.y. for the Xiatongling deposit, but with different cooling path rate. The Yashan deposit experienced a slow cooling rate (36.4 °C/m.y.) followed by a moderately rapid cooling rate (48.6 °C/m.y.), whereas the Xiatongling deposit had an early rapid cooling rate (74.1 °C/m.y.) followed by a slow cooling rate (29.7 °C/m.y.). Unlike porphyry Cu systems, the longevity of magmatic-hydrothermal process is not likely to be a key controlling factor for the total endowment and grade of W deposits. However, our analyses show that rapid cooling rates might facilitate formation of high grade stockwork and greisen W deposits.

Mica composition as a vector to gold mineralization: Deciphering hydrothermal and metamorphic effects in the Malartic district, Quebec

Canadian Malartic, with a total endowment of 16.3 Moz Au, is an important example of a large-tonnage, low-grade Archean gold deposit (current reserves of 204 Mt @ 1.08 g/t Au). It is located in the southern Superior Province in contact with, and immediately south of the east-west trending Cadillac-Larder Lake fault zone, which delineates the boundary between the Pontiac and Abitibi subprovinces. The deposit is hosted by Pontiac Group metaturbidites, Piché Group mafic-ultramafic metavolcanics and by porphyritic quartz monzodiorite to granodiorite that intruded these lithologies. The metamorphic grade increases southward from upper greenschist facies, which characterizes the immediate metamorphic environment of the Canadian Malartic deposit, to mid-amphibolite facies; the garnet isograd is crossed 1.5 km south of the deposit, and the staurolite isograd about one kilometer further south. Textural, structural and geochronological observations are consistent with a syn-kinematic (D2), early- to syn-peak metamorphic (M2) timing for the main ore-forming event.Mineralization in the metasedimentary rocks and porphyritic intrusions consists of disseminated native gold and minor gold-tellurides within stockworks of quartz-biotite-microcline-carbonate±pyrite veinlets (v2) and associated pervasive microcline-albite-biotite±(white mica)-carbonate-pyrite alteration. A zonal distribution of alteration is centered on structures that acted as preferential pathways for the hydrothermal fluids (e.g., Sladen Fault, NW-SE deformation zones). In the metasedimentary rocks, the proximal potassic alteration zone is dominated by microcline-albite±quartz with variable proportions of phlogopite (±white mica), carbonate minerals (calcite-ankerite±Fe-dolomite), quartz, pyrite and rutile. It grades outwards into a distal potassic-sericitic alteration zone characterized by relatively abundant Mg-rich biotite and phengitic white mica, as well as microcline, albite, quartz, calcite, pyrite and rutile. The zonal distribution of alteration features was due in part to a decrease in the total activity of sulfur species (∑aS) and oxygen fugacity (fO2) away from the main hydrothermal corridors, which is manifested by systematic changes in Fe-sulfide and (Fe-Ti)-oxide mineralogy.The effects of sulfidation (∑aS), oxidation (fO2) as well as K+, Fe2+ and H+ activity on biotite and white mica compositions were assessed from silicate-oxide-sulfide equilibria. Increasing ∑aS-fO2 conditions proximal to the hydrothermal fluid pathways caused pyrite to be stabilized over biotite, and iron sequestration in the sulfide phase in turn promoted the stability of magnesian biotite. Increasing sulfur metasomatism towards the hydrothermal centers was associated with systematic increases in biotite Mg# [Mg/(Fetotal+Mg)] and fluorine concentration, in agreement with the Fe-F avoidance principle. Alteration was also associated with a decrease in Al in biotite and white mica, coincident with increases in Si and Fe + Mg concentrations. These compositional trends were controlled by a Tschermak exchange reaction and are consistent with a gradual decrease in aK+ and/or pH upon progressive rock-buffering of a mildly alkaline, potassium-rich ore-forming fluid.Multicomponent phase equilibria (pseudosections), constrained for specified bulk rock compositions typical of non-mineralized Pontiac Group metasedimentary rocks, are used to model the expected composition of mica solid solutions under varying metamorphic P-T conditions. The thermodynamic modelling of biotite and white mica compositions suggests that the district-scale compositional trends documented for biotite and white mica along the metamorphic gradient, including the progression of the Tschermak substitution towards more aluminous compositions southwards, were likely the product of increasing metamorphic P-T conditions, rather than a distal effect of hydrothermal alteration.Mica mineral chemistry is clearly a sensitive indicator of hydrothermal and metamorphic processes at Canadian Malartic. Our results show that biotite and white mica compositions provide valuable tools that can be used to define hydrothermal fluid pathways in and around the deposit. These factors should be particularly useful for mapping the zonation of alteration features that characterize the footprint of major gold deposits in metamorphic terranes where micas typically display a spatial distribution ideal for defining mineral-chemical vectors to ore.

Efficient and strategy-proof allocation mechanisms in economies with many goods

In this paper, we show that in pure exchange economies where the number of goods equals or exceeds the number of agents, any Pareto-efficient and strategy-proof allocation mechanism always allocates the total endowment to some single agent even if the receivers vary.

How many boron minerals occur in Earth’s upper crust?

The current rate of discovery of new boron minerals (65 species or potential species described from 2008 to 2017) is higher than at any prior 10 year period, implying that rates of B mineral discovery could increase further with no obvious limit to boron mineral diversity in Earth’s crust. In contrast, large number of rare events (LNRE) models calculated from the 295 species of B minerals discovered through 2017 give a total predicted B mineral endowment in Earth’s crust of 459 ± 65.5 and 523 species, using a finite Zipf-Mandelbrot (fZM) model and Sichel’s generalized inverse Gauss-Poisson model (GIGP), respectively, i.e., there is a very real predicted limit of no more than ~500 species. As cautioned by Hazen, Hystad, and their co-authors, LNRE modeling presumes no changes in how minerals are discovered from the beginning of mineral discoveries in the late 18th century to early 2017. However this condition is clearly not the case, and thus changes could explain the discrepant indications. The most important changes are (1) the advent of the electron microprobe, which became widely used for chemical analysis of B minerals in 1978; (2) technological advances in single-crystal X-ray diffractrometry, (3) technological advances in electron microscopy including advent of electron backscattered diffraction; (4) advent of micro-Raman spectroscopy; and (5) changes in mineralogical nomenclatures, particularly of the tourmaline supergroup. Changes 1 to 4 are expected to reduce the size of the mineral grains that can be studied, thereby increasing the number of species accessible to study. Furthermore, should species have a fractal distribution (i.e., diversity is independent of scale) examination of increasingly smaller grains will turn up an even larger number of species. To evaluate the impact of these changes on the LNRE modeling, we modeled the 146 B minerals discovered up through 1978, which was selected as the cutoff because of (1) the important role played subsequently by the electron microprobe and (2) the number of species was 50% of the current number. This modeling gave 306 (fZM) and 359 (GIGP) for total species, i.e., the access to smaller grains afforded by advanced analytical instrumentation has resulted in an increased estimate of total endowment by 50% from 1978, whether the fZM or GIGP distribution is applied. We doubt that the ~500 B species estimate is the end of the story, as we expect there will be further technological advances in the future. A more realistic finale might come when we reach the natural limit imposed by the minimum number of unit cells needed for new mineral to be viable, and thus LNRE modeling might yet show that Earth’s total endowment of B minerals is finite. A review of past patterns of discovery of new boron minerals, which can inform us what to expect in future discoveries, reveal that only 19% of B minerals were synthesized prior to discovery. We conclude that synthetic compounds are not a particularly promising source of potential new B minerals. In contrast, 22% of B minerals were discovered prior to synthesis and 29% have unique structures, i.e., they have no synthetic analogs and are not isostructural with a known mineral. Accordingly, 41% of B minerals could not be predicted, and we conclude that the realm of as yet undiscovered B minerals holds a significant number of surprises.

Existence of equilibrium on asset markets with a countably infinite number of states

We consider a model with a countably infinite number of states of nature. The agents have equivalent probability beliefs and von Neumann–Morgenstern utilities. The No-Arbitrage Prices in this paper are, up to a scalar, the marginal utilities. We introduce the Beliefs Strong Equivalence and the No Half Line Condition of the same type conditions. Under these conditions, the No Arbitrage price condition is sufficient for the existence of an equilibrium when the commodity space is lp,1≤p<+∞. This No Arbitrage condition is necessary and sufficient for the existence of equilibrium when the total endowment is in l∞. Moreover, it is equivalent to the compactness of the individually rational utility set.

Deal or no deal? The effect of alcohol drinking on bargaining

Alcohol drinking during business negotiation is a very common practice, particularly in some East Asian countries. Does alcohol consumption affect negotiator's strategy and consequently the outcome of the negotiation? If so, what is the mechanism through which alcohol impacts negotiator's behavior? We investigate the effect of a moderate amount of alcohol on negotiation using controlled experiments. Subjects are randomly matched into pairs to play a bargaining game with adverse selection. In the game, each subject is given a private endowment. The total endowment is scaled up and shared equally between the pair provided that they agree to collaborate. It is found that a moderate amount of alcohol consumption increases subjects’ willingness to collaborate, thus improving their average payoff. We find that alcohol consumption increases neither subjects’ preference for risk nor altruism. A possible explanation for the increase in the likelihood of collaboration is that subjects under the influence of alcohol are more “cursed” in the sense of Eyster and Rabin (2005), which is supported by the estimation results of a structural model of quantal response equilibrium.

Optimal Control with State Constraint and Non-concave Dynamics: A Model Arising in Economic Growth

We consider an optimal control problem arising in the context of economic theory of growth, on the lines of the works by Skiba and Askenazy–Le Van. The framework of the model is intertemporal infinite horizon utility maximization. The dynamics involves a state variable representing total endowment of the social planner or average capital of the representative dynasty. From the mathematical viewpoint, the main features of the model are the following: (i) the dynamics is an increasing, unbounded and not globally concave function of the state; (ii) the state variable is subject to a static constraint; (iii) the admissible controls are merely locally integrable in the right half-line. Such assumptions seem to be weaker than those appearing in most of the existing literature. We give a direct proof of the existence of an optimal control for any initial capital \(k_{0}\ge 0\) and we carry on a qualitative study of the value function; moreover, using dynamic programming methods, we show that the value function is a continuous viscosity solution of the associated Hamilton–Jacobi–Bellman equation.

Fairness in an Ultimatum Game

We present a controlled laboratory environment in which we use an ultimatum game to generate two endogenous fairness indices. We use these as alternatives to the more conventional exogenous measure, the offer index, in a model of offer-acceptance which includes measures of social value orientations and risk attitudes as variables for explaining the acceptance or rejections of offers in an ultimatum game. In particular we are interested in providing an explanatory model which can support situations in which the likelihood to accept unfair offers (as measured by the offer index) will exceed the likelihood of rejecting a fair offer (again, as measured by the offer index). The offer index in the ultimatum game setting is the amount offered by a sender divided by the total endowment of the sender. Our endogenous fairness indices meet our condition of the likelihood of acceptance of an unfair offer exceeding the likelihood of rejecting a fair offer even though the explanatory power of the offer-acceptance models with the endogenous fairness indices is not significantly different from that with the exogenous fairness index.

New conditions for the existence of Radner equilibrium with infinitely many states

In atomless differential information economies, equilibria are known not to exist prevalently even when agents are risk averse expected utility maximizers. The notion of prevalence involves essentially picking an economy at random. In this paper, however, we establish existence results with economically meaningful assumptions on the information structure. We obtain existence when agents have independent information, and also when the total endowment of the economy is common knowledge.