Incentive Design and Pricing under Limited Inventory

44 Pages Posted: 22 Dec 2021 Last revised: 26 Apr 2024

See all articles by Ruiting Zuo

Ruiting Zuo

Fintech Thrust, the Society Hub, Hong Kong University of Science and Technology (GZ)

Tinglong Dai

Johns Hopkins University - Carey Business School; Johns Hopkins University - Hopkins Business of Health Initiative

Jussi Keppo

National University of Singapore (NUS) - NUS Business School

Date Written: April 25, 2024

Abstract

A firm faces random demand for a service it delivers on a given future date. To boost demand, the firm hires a sales agent who exerts unobservable effort continuously over time. The firm is concerned not only with increasing current demand, but also with smoothing demand over time to avoid losing goodwill if realized demand exceeds available inventory. We study the firm’s incentive design problem using a novel continuous-time principal-agent framework, in which demand drifts over time in response to an agent’s unobserved effort as well as the price the firm charges. To induce the agent’s sales effort, the firm chooses an incentive scheme that depends on the remaining inventory and the time to the service (e.g., time to departure in the case of airlines). We characterize the firm’s optimal incentive scheme under both static and dynamic pricing policies. Using parameters calibrated from the airline industry, we numerically show that under dynamic pricing, using a static incentive scheme helps the firm reap nearly all the benefits of the corresponding dynamic incentive scheme. Using a fully static strategy, on the other hand, results in a significant loss of efficiency. We also compare two partially dynamic strategies in which the firm uses dynamic pricing or dynamic contracting but not both. We show that when inventory levels are high and the demand is inelastic, the dynamic-contracting-only strategy outperforms the dynamic-pricing-only strategy; when inventory levels are low and the demand is elastic, however, the dynamic-pricing-only strategy outperforms the dynamic-contracting-only strategy.

Keywords: Incentive design, moral hazard, pricing, limited inventory, marketing-operations interface

JEL Classification: C63, D82, E2, L11

Suggested Citation

Zuo, Ruiting and Dai, Tinglong and Keppo, Jussi, Incentive Design and Pricing under Limited Inventory (April 25, 2024). Available at SSRN: https://ssrn.com/abstract=3989971 or http://dx.doi.org/10.2139/ssrn.3989971

Ruiting Zuo

Fintech Thrust, the Society Hub, Hong Kong University of Science and Technology (GZ) ( email )

+86 18256944842 (Phone)

Tinglong Dai (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

HOME PAGE: http://carey.jhu.edu/faculty/faculty-directory/tinglong-dai-phd

Johns Hopkins University - Hopkins Business of Health Initiative ( email )

100 International Drive
Batlimore, MD 21202
United States

HOME PAGE: http://hbhi.jhu.edu/expert/tinglong-dai

Jussi Keppo

National University of Singapore (NUS) - NUS Business School ( email )

Mochtar Riady Building
15 Kent Ridge Drive
Singapore, 119245
Singapore

HOME PAGE: http://https://www.jussikeppo.com

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