Hedging Effect of Low-Quality Capital Assets in Competitive Industries

Abstract

We highlight the impact of capital quality, i.e., the depreciation rate of capital assets, on firms' investment behavior, 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 depreciates faster and, thus, requires a higher level of reinvestment. In equilibrium, competitive firms may show a higher willingness to pay for the low-quality capital since depreciation provides an embedded hedge feature for the firm value. In particular, we show that demand elasticity is one of the key determinants of the willingness to pay; ceteris paribus, firms may prefer a high-quality capital in a market with high price elasticity of demand and the low-quality capital in a market with highly inelastic demand. 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.