EURO 2024 Copenhagen
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941. Revenue Functions Are Nonconcave in the Inputs When the Technology is Nonconvex: The Unbearable Lightness of Convexification

Invited abstract in session WD-48: DEA methodological developments II, stream Data Envelopment Analysis and its Application.

Wednesday, 14:30-16:00
Room: 60 (building: 324)

Authors (first author is the speaker)

1. Kristiaan Kerstens
IESEG School of Management, CNRS-LEM (UMR 9221)
2. Oleg Badunenko
University of Portsmouth
3. Jafar Sadeghi
Ivey Business School, Western University, London Ontario

Abstract

Revenue functions are studied under the assumption that the technology is nonconvex. More specifically, we show theoretically that the convex revenue functions are larger or equal to the nonconvex revenue functions. However, with one input and constant returns to scale (CRS) technologies, both these revenue functions coincide. Including more inputs or varying returns to scale assumption (e.g., variable returns to scale, VRS) results in differences between the convex and nonconvex revenue functions. We use USA state-level agricultural data to showcase our theoretical result empirically. We first visualize the revenue functions under constant and variable returns to scale assumptions and demonstrate that the former is identical irrespective of whether technology is convex or nonconvex while the latter revenue functions are different. We further show graphically that the convex or nonconvex revenue functions are different both under CRS and VRS with 4 inputs. Additionally, we use statistical tests (equality of densities and stochastic dominance) to show that the convex or nonconvex revenue functions are statistically different. Finally, we perform scale efficiency analysis to show how using the convexity assumption may result in false policy implications.

Keywords

Status: accepted

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