New conservation laws in a neoclassical von Neumann model

Article Abstract:

Samuelson's Von Neumann model is generalized to incorporate a discount rate and the prices of investment goods. Working from the Noether theorem, two conservation laws are obtained. They concern the constancy of the discounted value of wealth and the constancy of discounted income. Other results demonstrate the derivation of solutions without the use of Euler-Lagrange equations, the constancy of prices and the validity of Samuelson's hypothesis concerning the ratio of income to wealth and the maximal balanced growth.

Usage, Wealth, National income, Von Neumann algebras, Conservation laws (Physics)

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Ultraproducts and aggregation

Article Abstract:

Arrow's social choice theorem is investigated within the framework of model theory and first-order logic. Specifically, Arrow-type aggregators of preferences and the ultraproducts are proven to coincide over ultrafilters. To understand the loss of continuity of products under aggregation, Los' theorem is used to obtain a rule for identifying whether a property is lost during aggregation. Subsequently, the Ax theorem is advanced to explain the arbitrariness of Arrow-type aggregators.

Consumer preferences, Model theory, Social choice

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Time-neutrality and linearity

Article Abstract:

Time-neutrality and impatience in a finite horizon context are well-understood economic concepts. However, time-neturality on the set of bounded infinite utility streams remains undefined. Time-neutrality in an infinite horizon results from the repeated application of time-neutrality's finite version. Research shows that time-neutrality's infinite version can be defined as invariance under bounded permutations.

Economic research, Infinite, Infinity (Mathematics)

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