Concept-domino

Ole Peters, London Mathematical Laboratory, London, UK

Supposedly, science and mathematics are of limited use in economics because
of the human element, because the system responds to attempts of modelling
it, because the effort is self-referential. My experience of difficulties
in economics is different. Failing to replicate foundational results in the
field, I have found that a number of problems are unresolved because
economics got the mathematics wrong. In seminal papers from the 1700s to
the 2000s basic mathematical errors have been propagated. The errors
invalidate fundamental theorems.

Starting with the simple observation that no stochastic growth process is
ergodic, I show a sequence of "big results" in economics that are
undermined and topple in domino-like fashion. Part of this can be
understood historically. Leading economists explicitly restricted formal
economics to ergodic equilibrium models; since such models bear no
resemblance to the actual economy, non-ergodic far-from equilibrium models
are used in practice (the random walk was invented here). The result is
conceptually self-contradictory and mathematically flawed.

In the seminar I will resolve the leverage problem and the St Petersburg
paradox. I will show that Bernoulli (1738) made a small error that was
corrected by Laplace (1814). The error was re-introduced by Menger (1934)
and incorporated in v. Neumann and Morgenstern's (1944) axiomatic
formulation of utility theory. From there it propagated to decision theory,
game theory and thereby all major branches of economics. I will list
further questions that we have addressed. I conclude that economics is
hard, but less hard once basic mathematical errors are corrected.