The determination of the price of capital goods: A differential game approach

In this paper, building upon a q-model of investment with adjustment costs, we address the strategic determinants of the price of newly installed productive capacity. Specifically, we develop a differential game in which a competitive producer of consumption goods deals with a seller of capital goods endowed with market power. From a theoretical perspective, we show that an open-loop Stackelberg equilibrium with non-cooperative features requires the producer of consumption goods to be more impatient than the seller of capital goods. Thereafter, relying on some numerical simulations, we show that our theoretical setting is able to replicate the countercyclical pattern of the relative price of capital goods as well as its negative relationship with the investment-output ratio.