Boyan Jovanovic and Jan Eeckhout
in Journal of Economic Theory Vol. 147, No. 2, 551 - 569.
We study an economy in which firms use labor and various vintages of capital in a CES production function for the final good. We explicitly solve for the investment in capital of a given vintage as a function of its age, and for the resulting stocks of capital. We show that for reasonable parameter values, inverted-U- shaped dynamics of investment and S-shaped dynamics for capital arise in equilibrium. We view the model as an explanation of intra-firm adoption lags, i.e., the observation that firms adopt innovations over time and not instantaneously.