Question: Paul Samuelson (Foundations of Economic Analysis, p. 5) wrote: "In this study I attempt to show that ... the conditions of equilibrium are equivalent to the maximization (minimization) of some magnitude. ... However, when we leave single economic units, the determinination of unknowns is found unrelated to an extremum position. In even the simplest business cycle theories there is lacking symmetry in the condition of equilibrium so that there is no possibility of directly reducing the problem to that of a maximum or a minimum." Discuss the Samuelson statement in view of the discussion about symmetry, integrability, and equilibrium developed in this book.