Technology Adoption: Optimal Timing, Pricing, and Employee Incentives
69 Pages Posted: 24 Sep 2019 Last revised: 28 Oct 2019
Date Written: October 27, 2019
With the rapid development of new technologies, firms and technology suppliers must understand the timing, pricing, and incentive issues regarding technology adoption. This paper formulates a general continuous time Stackelberg game to characterize the pricing and adoption decisions of a new technology between the supplier and the firm, under the consideration of the incentive issues of employees. The new technology can either increase the firm's productivity, decrease its running cost, or do both. Among the three players, the supplier (leader) first offers the new technology at a price, the firm (follower) then decides whether and when to adopt the technology, and each employee of the firm decides whether to use the technology or not (if the firm adopts). Each employee who decides to use this new technology would encounter a stochastic learning cost, and hence not all of them would use it. First, we are able to obtain the closed-form solution of the firm's optimal adoption decision. In particular, we characterize the threshold adoption policy and three adoption regions (no adoption, full adoption, and partial adoption region). Next, we consider the design of incentive wage contract to motivate the technology adoption among employees. We find that it is always optimal to adjust the piece-rate alone instead of jointly adjust the base salary and piece-rate in terms of firm’s revenue. Finally, we characterize the supplier's equilibrium price and present the sensitivity analyses. We show numerically that the supplier's equilibrium price is lower by adjusting the piece-rate as compared to adjusting the base salary; however, its revenue is always higher. At the end, we extend our main model with the impact of employees' learning time and quality uncertainty of the new technology. We find that employees' learning time delays technology adoption and the quality uncertainty can either decrease or increase the firm's adoption time.
Keywords: optimal stopping time, Stackelberg game, technology, adoption, pricing, incentive, wage
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