An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

Ad valorem housing subsidies may reduce house building

In this paper it is shown that an ad valorem housing subsidy set by a central regulator (or a raise in the ad valorem housing subsidy rate) may reduce the number of houses built in the market and increase the price paid by the buyers of houses. The analysis considers a situation where there is imperfect competition in the housing market and a local regulator that decides on density, or on the number of sites for housing development, and that cares about a combination of the profits of housing developers and the surplus of buyers of houses.