Schumpeter's paradox reconsidered: The need for a theory of circular flow

This study focuses on the well-known theme of Schumpeter’s system of economic theory. Specifically, the study discusses Schumpeter’s paradoxical stance on Walras’ general equilibrium theory, which Louçã (1997) called Schumpeter’s paradox. We reconsider the significance of the notion of circular flow in business cycle theory, after recognising the continuity from static to dynamic theory, and then to business cycle theory that integrates these theories. In doing so, we focus on the fact that Schumpeter called the equilibrium in the cyclical process a circular flow or a stationary process and proposed his own concept of neighbourhoods of equilibrium, which was not found in Walras’ general equilibrium theory. Through such an analysis, we propose that Schumpeter’s paradox is eased to some degree and that the theory of circular flow should be explored further

Simulations of Wide-Field Weak Lensing Surveys II: Covariance Matrix of Real Space Correlation Functions

Using 1000 ray-tracing simulations for a {\Lambda}-dominated cold dark model in Sato et al. (2009), we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in the previous measurements. The shear correlation function of a particular separation angle is affected by Fourier modes over a wide range of multipoles, even beyond a survey area, which complicates the analysis of the covariance matrix. To overcome such obstacles we first construct Gaussian shear simulations from the 1000 realizations, and then use the Gaussian simulations to disentangle the Gaussian covariance contribution to the covariance matrix we measured from the original simulations. We found that an analytical formula of Gaussian covariance overestimates the covariance amplitudes due to an effect of finite survey area. Furthermore, the clean separation of the Gaussian covariance allows to examine the non-Gaussian covariance contributions as a function of separation angles and source redshifts. For upcoming surveys with typical source redshifts of z_s=0.6 and 1.0, the non-Gaussian contribution to the diagonal covariance components at 1 arcminute scales is greater than the Gaussian contribution by a factor of 20 and 10, respectively. Predictions based on the halo model qualitatively well reproduce the simulation results, however show a sizable disagreement in the covariance amplitudes. By combining these simulation results we develop a fitting formula to the covariance matrix for a survey with arbitrary area coverage, taking into account effects of the finiteness of survey area on the Gaussian covariance.Comment: 12 pages, 12 figures, accepted for publication in the Astrophysical Journal. Simulation data (1000 convergence power spectra and cosmic shear correlation functions for {\xi}+({\theta}) and {\xi}-({\theta})) are available upon request (contact [email protected]