Yield and Area Elasticities. A Cost Function Approach with Uncertainty

This paper develops a method to jointly estimate crop yield elasticities and area elasticities with respect to output prices based on a theoretically consistent model. The model uses a duality theory approach for the multi-output and multi-input firm, and introduces uncertainty in the level of target output which conditions the cost minimization problem, in the output prices and in the conditional input demand functions. The underlying production technology is conditioned on fixed inputs, both allocatable and non-allocatable. Up to our knowledge, there have been no theoretical developments of this type of models for multioutput technologies. Our approach is also novel because no previous model of this type has introduced the effects of allocatable fixed inputs. We provide an empirical application of this theoretical framework using State-level data and approximating the dual cost function by a normalized quadratic flexible functional form. We derive expressions for the elasticities of interest conditional on the function specification assumed.yield elasticities, area elasticities, duality theory, cost function, uncertainty, Production Economics,

Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

Understanding interdependency through complex information sharing

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work, we propose to analyze these interactions as different modes of information sharing. Towards this end, we introduce a novel axiomatic framework for decomposing the joint entropy, which characterizes the various ways in which random variables can share information. The key contribution of our framework is to distinguish between interdependencies where the information is shared redundantly, and synergistic interdependencies where the sharing structure exists in the whole but not between the parts. We show that our axioms determine unique formulas for all the terms of the proposed decomposition for a number of cases of interest. Moreover, we show how these results can be applied to several network information theory problems, providing a more intuitive understanding of their fundamental limits.Comment: 39 pages, 4 figure