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Mathematics Colloquium

Stevens Institute of Technology

Title: Why a Competitive Industry May Prefer Low-Quality Assets
Date: Monday, April 15, 2019 (note special day)
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. We highlight the impact of capital quality, i.e., depreciation rate of capital assets, on firms' investment behavior, the endogenous output price dynamics, and industry equilibrium outcomes. To rigorously examine this question, a continuous-time model of dynamic capacity investment under uncertainty is presented where the spot price of a depreciating capital asset is determined in a market equilibrium. The lower-quality (shorter-lived) capital is cheaper to purchase but depreciates faster and requires a higher level of reinvestment. In equilibrium, competitive firms may show a high willingness to pay for the capital of low quality, since depreciation provides an embedded hedge feature for the firm value. We derive closed-form solutions for the optimal investment policies as well as the steady-state distribution of endogenous output prices and the dynamics of aggregate capital in the economy. We also show that with incremental investment and marked-to-market capital goods prices, the net present value of new investment opportunities is always equal to zero.