Private Versus Public Health Care in a National Health Service

This paper study the interplay between private and public health care in a National Health Service. We consider a two-stage game, where at stage one a Health Authority sets the public sector wage and a subsidy to (or tax on) private provision. At stage two physicians decide how much to work in the public and the private sector. We characterise different equilibria depending on the Health Authority's objectives, the physicians' job preferences, and the cost efficiency of private relative to public provision of health care. We find that the scope for a mixed health care system is limited when physicians are indifferent between working in the public and private sector. Competition between physicians triggers a shift from public provision towards private provision, and an increase in the total amount of health care provided. The endogenous nature of labour supply may have counter-intuitive effects. For example, a cost reduction in the private sector is followed by a higher wage in the public sector.health care, mixed oligopooly, physicians

Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes

In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear $H_\infty$ estimate.Comment: 14 pages, several references added, remarks section added, clarified constructio

Change-over within little scope: On the decision neutrality of recent tax reform proposals

Political economy aspects make progressive income taxation and taxation of capital income imperative in practise. International tax competition and profit shifting, in turn, put pressure on corporate and capital taxes. Hence, the scope for a politically feasible change-over to a status of improved taxation is little. We provide an extended dynamic general equilibrium model and analyze politically feasible recent reform proposals referring neutrality. We then propose an alternative tax reform that, in contrast to these proposals, guarantees even growth neutrality, without necessarily jeopardizing political feasibility.Dynamic general equilibrium models; taxation; tax reform; decision neutrality; ACE; dual income tax

Quantifying the Fragility of Galactic Disks in Minor Mergers

We perform fully self-consistent stellar dynamical simulations of the accretion of a companion ("satellite") galaxy by a large disk galaxy to investigate the interaction between the disk, halo, and satellite components of the system during a merger. Our fiducial encounter begins with a satellite in a prograde, circular orbit inclined thirty degrees with respect to the disk plane at a galactocentric distance of six disk scalelengths. The satellite's mass is 10% of the disk's mass and its half-mass radius is about 1.3 kpc. The system is modelled with 500 000 particles, sufficient to mitigate numerical relaxation noise over the merging time. The satellite sinks in only ~1 Gyr and a core containing ~45% of its initial mass reaches the centre of the disk. With so much of the satellite's mass remaining intact, the disk sustains significant damage as the satellite passes through. At the solar circle we find that the disk thickens ~60%, the velocity dispersions increase by \Delta\mbox{\boldmath\sigma} \simeq (10,8,8) km/s to $(\sigma_R, \sigma_\phi, \sigma_z) \simeq (48, 42, 38)$ km/s, and the asymmetric drift is unchanged at ~18 km/s. Although the disk is not destroyed by these events (hence "minor" mergers), its final state resembles a disk galaxy of earlier Hubble type than its initial state, thicker and hotter, with the satellite's core enhancing the bulge. Thus minor mergers continue to be a promising mechanism for driving galaxy evolution.Comment: LaTeX with AASTeX macros; text only. For PostScript with figures embedded, go to http://www.ucolick.org/~iwalker/ss