A possible pitfall in textbook examples of the two-team league with equal-proportion gate revenue sharing

Abstract

Problem statement and purpose:For pedagogical purposes, textbooks and papers often use a simple two-team league to analyse the consequences on competitive balance and wage level formation from equal-proportion gate revenue sharing. In a profit-maximizing regime with a closed labour market, it is often assumed that this situation produces identical negative parallel shifts in the linear marginal revenue curves of the teams. This paper aims to analyse the validity of the abovementioned statement. Approach: The analysis isperformedby mathematical approaches. Results: This paper shows that the negative shifts are parallel and identical only when the slope coefficients are equal. Conclusions: In an educational context, confusions occur because of inconsistencies between theoretical textbook explanations and numerical student tasks. This paper aims to explain the negative shift theoretically and numerically in a mannerthat avoids this confusion. Furthermore, this paper shows mathematically that the parallel and identical shifts of the marginal revenue functions are only a special case.