Is Optimal Pricing a Myth From Business Calculus? Is Business Calculus an Oxymoron?

Abstract

Professor Dudley's question is answered in the present essay. 1. MATHEMATICAL SOClEl'lES SHOW COUNTEEPLES TO ONI PRICING. Firstly, publishers may eschew mathematics in setting rates because they may be following their mathematics professors' counterexamples. Indeed, none of the dues statements for 1995 from the American Mathematical Society (AMS), Mathematical Association of America (MAA), and Society for Industrial and Applied Mathematics (SIAM) offers any discount to members of less than sixty years of age for payments covering more than one year of subscrip- tion. Moreover, while these societies send advanced notices requesting early renewal, none offers any discount for early payments either, which corroborates a paraphrase of Professor Dudley's findings: Three magazines in the sample (Bulletin of the AMS, American Mathemati- cal Monthly, and SlAM Review) give no discount at all, completely disregard- ing their readers' ability to make calculations of present values. (Italics substituted.) Moving from present to future values, observe that the MAA's dues increased from $122 to $128 (for all three MAA journals) from the dues notice sent in 1993 to the notice sent in 1994, a relative increase of about 4.92%, which exceeds twice the annual rate of inflation for that period, about 2.3% (2), thus causing a real price increase (Fisher's effect (19)) of about (0.049 - 0.023)/1.023 2.59%, which campus representatives must now sell to their librarian. Furthermore, the discontinuous rate schedules of the AMS and MAA give members financial incentives to understate their annual professional income by imposing large surcharges for small increases in income: the AMS dues jump from $87 to $116 as income jumps from $45,000 to $45,000.01, corresponding to a marginal income-tax rate of (116 - 87)/0.01 = 290,000%, while the MAA dues jump from $128 to $159 as income jumps from $50,000 to $50,00Q.01, correspond- ing to a marginal income-tax rate of (159 - 128)/0.01 = 310,000%.