Incomplete markets with no Hart points

We provide a geometric test of whether a general equilibrium incomplete markets (GEI) economy has Hart points---points at which the rank of the securities payoff matrix drops. Condition (H) says that, at each nonterminal node, there is an affine set (of appropriate dimension) that intersects all of a well-specified set of convex polyhedra. If the economy has Hart points, then Condition (H) is satisfied; consequently, if condition (H) fails, the economy has no Hart points. The shapes of the convex polyhedra are determined by the number of physical goods and the dividends of the securities, but are independent of the endowments and preferences of the agents. Condition (H) fails, and thus there are no Hart points, in interesting classes of economies with only short-lived securities, including economies obtained by discretizing an economy with a continuum of states and sufficiently diverse payoffs.Incomplete Markets, GEI model, Hart points

Examining the Impact of Parental Socialization on the Coping Styles of Black Graduate Students Faced with Microaggressions

This article explores case examples of two graduate students who endure microaggressions from their math professor at a predominantly White university. The role that parental socialization plays in how these students developed their racial identities and the coping strategies they employed, is analyzed through the lens of Triple Quandary theory (Boykin and Toms 1 985). Findings from this investigation suggest that parental socialization is critical in preparing these students to cope with and respond to microaggressions in protective and adaptive ways. This paper illuminates coping styles, although divergent, that served these graduate students\u27 needs and protected their individual racial identities. Further, the support these students received from their faculty advisor who is also Black, exemplifies the importance of mentorship and advocacy from faculty of color to Black college students\u27 success. Direction for continuity in parental teachings for K-12 and university level educators are discussed

Simultaneous measurements of particulate and gas-phase water-soluble organic carbon concentrations at remote and urban-influenced locations

The sources, sinks, and overall importance of watersoluble organic carbon (WSOC) in the atmosphere are not well understood. Although the primary historical focus has been on particulate WSOC (WSOCP), here we also present results obtained using a newly developed technique that additionally measures gas-phase water-soluble organic carbon (WSOCG). These first-of-their-kind measurements show that WSOCG can often be more than ten times larger than WSOCP at both urban and remote locations. The average fraction of WSOC residing in the gas phase (fg = WSOCG/(WSOCG + WSOCP)) at five various field sites ranged from 0.64 to 0.93, implying significant differences in WSOC phase partitioning between locations. At Houston, TX, and Summit, Greenland, a repeatable diurnal pattern was observed, with minimum values for fg occurring at night. These trends likely are due, at least in part, to temperature and/or relative humidity related gas-to-particle partitioning. These coincident measurements of WSOC in both the gas and particle phases indicate that a relatively large reservoir of water-soluble organic mass is not taken into account by measurements focused only on WSOCP. In addition, a significant amount of WSOCG is available to form WSOCP or enter cloud droplets depending on the chemical and physical properties of the droplets and/or aerosols present. Citation: Anderson, C., J. E. Dibb, R. J. Griffin, and M. H. Bergin (2008), Simultaneous measurements of particulate and gas-phase water-soluble organic carbon concentrations at remote and urban-influenced locations, Geophys. Res. Lett., 35, L13706, doi:10.1029/2008GL033966

Core Theory with Strongly Convex Preferences

We consider economies with preferences drawn from a very general class of strongly convex preferences, closely related to the class of convex (but intransitive and incomplete) preferences for which Mas-Colell proved the existence of competitive equilibria [13]. We prove a strong core limit theorem for sequences of such economies with a mild assumption on endowments (the largest endowment is small compared to the total endowment) and a uniform convexity condition. The results extend corresponding results in Hildenbrand’s book [8]. The proof, which is based on our earlier result for economies with more general preferences [2], is elementary

Strong Core Theorems with Nonconvex Preferences

It is known that in large economies with strongly convex preferences, the commodity bundles agents receive at core allocations are near their demand sets. Without convexity, it is know that agents need not be near their demand sets, although they will satisfy a weaker condition. In this paper, we show that, for “most” economies (in the sense of probability and in the sense of the Baire category theorem), the stronger form of approximation holds without convexity