Payback without apology

Digit Reversal Without Apology

In A Mathematician’s Apology [1] G. H. Hardy states, “8712 and 9801 are the only four-figure numbers which are integral multiples of their reversals”; and, he further comments that “this is not a serious theorem, as it is not capable of any significant generalization.” However, Hardy’s comment may have been short-sighted. In 1966, A. Sutcliffe [2] expanded this obscure fact about reversals. Ins...

Partial Adjustment Without Apology

Many kinds of economic behavior appear to be governed by discrete and occasional individual choices. Despite this, econometric partial adjustment models perform relatively well at the aggregate level. Analyzing the classic employment adjustment problem, we show how discrete and occasional microeconomic adjustment is well described by a new form of partial adjustment model that aggregates the ac...

Sincere Apology Without Morai Responsibility

Alice is a moral responsibility abolitionist. She firmly believes that no one (including herselO is ever morally responsible, that rewards and punishments can never be justified on the basis of just deserts, and that blaming people for vicious character traits and vile acts is never morally justified. One day, Barbara, Alice's dearest friend, confides to Alice a special secret: a secret Barbara...

Competitive rational expectations equilibria without apology

In a standard financial market model with asymmetric information with a finite number N of risk-averse informed traders, competitive rational expectations equilibria provide a good approximation to strategic equilibria as long as N is not too small: equilibrium prices in each situation converge to each other at a rate of 1/N as the market becomes large. The approximation is particularly good wh...

Apology