On the flexible functional forms

This note proposes a general structure of the so-called "flexible functional forms" able to describe direct utility functions. It is obtained by solving the functional equation: f[U(x₁, x₂, ..., xn)]=H[f(x₁), f(x₂), ..., f(xn)] under two different sets of hypotheses. Moreover, some results are stated to garantee the monotonicity and the strict quasiconcavity of the utility function, according to the neoclassical theory. Finally it is showed how the best known functional forms as the CES, the Translog and the Cobb Douglas can be seen as particular cases of the model proposed, verifying which of them satisfy the found conditions for the monotonicity and the strict quasiconcavity of the utility function