Law, Property, and Marital Dissolution

This paper challenges the view that legal rights are not important in affecting whether people divorce, but it puts as much emphasis on property rights (given, for example, by the law on alimony) as on dissolution rights. The paper sets out two stylised models of marriage and examines the consequences of fuller compensation for economic sacrifices made during marriage. If the dominant economic issue in a marriage is who undertakes household tasks then a law giving fuller compensation makes divorce more likely. If the dominant issue is child custody, divorce is less likely.Marriage, Divorce, Property rights, Household production, Child custody

Uniqueness of Equilibrium in Two-sided Matching

This paper analyses a sufficient condition for uniqueness of equilibrium in two-sided matching with non-transferable utility. The condition is easy to interpret, being based on the notion that a person’s characteristics both form the basis of their attraction to the opposite sex, and determine their own sexual preferences.Uniqueness, matching, marriage.

Property Rights and the Economics of Divorce

With examples drawn from English and Scots law, this paper sets up a simple framework to analyse the role of property and dissolution rights in determining divorce decisions. Although firmly based on the economic analysis of choice and bargaining, the discussion is relatively non-technical and directed at drawing out implications for public policy. In particular the paper emphasises the importance of the laws on alimony and property division after divorce in affecting not only divorce decisions but also the allocation of resources within surviving marriages.

Samuelson machines and the optimal public-private mix

Standard economic analysis assumes the sets of public and private goods to be exogenously given. Yet societies very often choose the public-private mix, using resources to convert seemingly private goods into ones with public goods characteristics and vice versa. In practice, we see a bewilderingly large variety of public-private mixes across societies. This papers advances an analysis of the choice of the public-private mix in the framework of voluntary contributions to public goods provision, by envisaging that, starting from a situation where all goods have private characteristics, some goods can be changed to have public goods characteristics at a cost (by purchasing a "Samuelson machine"). It characterizes the jointly optimal choice of the public-private mix and the efficient supply or not of the public goods in the mix. This characterization generates a number of testable predictions on the public-private mix, and on the prevalence of free riding

On column density thresholds and the star formation rate

We present the results of a numerical study designed to address the question of whether there is a column density threshold for star formation within molecular clouds. We have simulated a large number of different clouds, with volume and column densities spanning a wide range of different values, using a state-of-the-art model for the coupled chemical, thermal and dynamical evolution of the gas. We show that star formation is only possible in regions where the mean (area-averaged) column density exceeds $10^{21} \: {\rm cm^{-2}}$. Within the clouds, we also show that there is a good correlation between the mass of gas above a K-band extinction $A_{\rm K} = 0.8$ and the star formation rate (SFR), in agreement with recent observational work. Previously, this relationship has been explained in terms of a correlation between the SFR and the mass in dense gas. However, we find that this correlation is weaker and more time-dependent than that between the SFR and the column density. In support of previous studies, we argue that dust shielding is the key process: the true correlation is one between the SFR and the mass in cold, well-shielded gas, and the latter correlates better with the column density than the volume density.Comment: 21 pages and 12 figures. Accepted for publication in MNRA

Is atomic carbon a good tracer of molecular gas in metal-poor galaxies?

Carbon monoxide (CO) is widely used as a tracer of molecular hydrogen (H2) in metal-rich galaxies, but is known to become ineffective in low metallicity dwarf galaxies. Atomic carbon has been suggested as a superior tracer of H2 in these metal-poor systems, but its suitability remains unproven. To help us to assess how well atomic carbon traces H2 at low metallicity, we have performed a series of numerical simulations of turbulent molecular clouds that cover a wide range of different metallicities. Our simulations demonstrate that in star-forming clouds, the conversion factor between [CI] emission and H2 mass, $X_{\rm CI}$, scales approximately as $X_{\rm CI} \propto Z^{-1}$. We recover a similar scaling for the CO-to-H2 conversion factor, $X_{\rm CO}$, but find that at this point in the evolution of the clouds, $X_{\rm CO}$ is consistently smaller than $X_{\rm CI}$, by a factor of a few or more. We have also examined how $X_{\rm CI}$ and $X_{\rm CO}$ evolve with time. We find that $X_{\rm CI}$ does not vary strongly with time, demonstrating that atomic carbon remains a good tracer of H2 in metal-poor systems even at times significantly before the onset of star formation. On the other hand, $X_{\rm CO}$ varies very strongly with time in metal-poor clouds, showing that CO does not trace H2 well in starless clouds at low metallicity.Comment: 16 pages, 9 figures. Updated to match the version accepted by MNRAS. The main change from the previous version is a new sub-section (3.6) discussing the possible impact of freeze-out and other processes not included in our numerical simulation

Strongly graded groupoids and strongly graded Steinberg algebras

We study strongly graded groupoids, which are topological groupoids $\mathcal G$ equipped with a continuous, surjective functor $\kappa: \mathcal G \to \Gamma$, to a discrete group $\Gamma$, such that $\kappa^{-1}(\gamma)\kappa^{-1}(\delta) = \kappa^{-1}(\gamma \delta)$, for all $\gamma, \delta \in \Gamma$. We introduce the category of graded $\mathcal G$-sheaves, and prove an analogue of Dade's Theorem: $\mathcal G$ is strongly graded if and only if every graded $\mathcal G$-sheaf is induced by a $\mathcal G_{\epsilon}$-sheaf. The Steinberg algebra of a graded ample groupoid is graded, and we prove that the algebra is strongly graded if and only if the groupoid is. Applying this result, we obtain a complete graphical characterisation of strongly graded Leavitt path and Kumjian-Pask algebras