Capital Reallocation and Growth

Heterogeneity is ubiquitous in firm-level and sectoral data. Equilibrium models, however, typically assume a representative firm, as in Andrew B. Abel and Olivier J. Blanchard (1983). The representative firm paradigm leaves no role for the distribution of capital. We model capital reallocation in a general equilibrium model with two sectors. Capital adjustment costs capture illiquidity in our model, similar to Hirofumi Uzawa’s (1969) capital installation technology. We follow Fumio Hayashi (1982) in assuming that the production technology is linearly homogeneous, which allows us to focus on the sectoral distribution of capital, separately from the level of total capital. The two sectors may have different levels of productivity, and we show that the distribution of capital between the two sectors is the single state variable governing investment, growth, and valuation in the economy. We analytically characterize prices and quantities, including investment, growth, the interest rate, and the price of capital (Tobin’s q) at both aggregate and sectoral levels, along with the effects of sectoral heterogeneity and reallocation in the economy. Without adjustment costs, capital is immediately reallocated to the more productive sector. With adjustment costs, the central planner optimally trades off growth against the cost of reallocating capital. Hence, reallocation to the high productivity sector is not immediate, Capital Market FriCtions and liquidity †