Antonelli's analytical techniques: their exploitation to derive results in duality theory

Antonelli, over a hundred years ago, pioneered techniques of economic analysis which still can be usefully employed to provide apparently new insights in duality theory. This assertion is demonstrated through the applications of these techniques to derive specific results in duality theory. These applications allow an apparently new derivation of the equality between the partial derivative of the expenditure function, with respect to the price of some good, and the compensated level of demand for this good. In addition, use of Antonelli's analytical techniques reveals links between certain results in duality theory that, apparently, have not been noticed before in the relevant literature.