Nataf’s Theorem, Taylor’s Expansion and Homogeneity in Consumer Demand
Macrorelations should obey Nataf’s specification requirements to be decomposable into microrelations. Taylor expansions can command such obedience and indicate the omissions if approximations are used. This paper discusses in section 3 how additional restrictions such as equilibrium conditions can be incorporated in a Taylor framework to increase the variety of possible specifications. In section 4 it is shown how this variety shrinks if the condition of homogeneity must be satisfied. As such it may help to clarify some points of Gorman’s (1981) general theorems on Engel curves. At the same time an inaccuracy in his paper is indicated.
Aggregation of economic relations: A note
SummaryThis note considers aggregation of economic relations over individuals, where individual behavior differs according to individual characteristics, such as income, wealth and tastes. Assuming a multivariate distribution of these characteristics among individuals, aggregate per capita behavior is approximated in terms of the behavior of the average individual, plus a term depending on the nonlinearity of the relation and the covariance matrix of the distribution of the characteristics.
The microscale obstacle-resolving meteorological model MITRAS v2.0: model theory
Abstract. This paper describes the developing theory and underlying
processes of the microscale obstacle-resolving model MITRAS version 2. MITRAS
calculates wind, temperature, humidity, and precipitation fields, as well as
transport within the obstacle layer using Reynolds averaging. It explicitly
resolves obstacles, including buildings and overhanging obstacles, to
consider their aerodynamic and thermodynamic effects. Buildings are
represented by impermeable grid cells at the building positions so that the
wind speed vanishes in these grid cells. Wall functions are used to calculate
appropriate turbulent fluxes. Most exchange processes at the obstacle
surfaces are considered in MITRAS, including turbulent and radiative
processes, in order to obtain an accurate surface temperature. MITRAS is also
able to simulate the effect of wind turbines. They are parameterized using
the actuator-disk concept to account for the reduction in wind speed. The
turbulence generation in the wake of a wind turbine is parameterized by
adding an additional part to the turbulence mechanical production term in the
turbulent kinetic energy equation. Effects of trees are considered
explicitly, including the wind speed reduction, turbulence production, and
dissipation due to drag forces from plant foliage elements, as well as the
radiation absorption and shading. The paper provides not only
documentation of the model dynamics and numerical framework but also a solid
foundation for future microscale model extensions.
