Capital expansion and reduction with fixed and proportional costs under demand ambiguity

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Abstract

This study investigates the capital expansion and reduction problem in firms when the output demand is ambiguous. We use the concept of κ-ignorance to describe the output demand ambiguity. When a firm changes its level of capital, it incurs both fixed and proportional costs. Therefore, the firm's problem is formulated as a stochastic impulse control problem. We solve the firm's problem via quasi-variational inequalities and numerically derive an optimal capital expansion and reduction policy. Further, we numerically conduct a comparative statics analysis that confirms that output demand ambiguity promotes capital reduction, while delaying capital expansion. Additionally, combining both the effects shrinks the continuation region.

Journal

  • 同志社商学

    同志社商学 72 (6), 1209-1227, 2021-03-12

    The Association of Commerce Doshisha University

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