A microfoundation of the Harrod–Okishio investment function

The Harrod–Okishio investment function was proposed by Nobuo Okishio. It typically causes unconditional instability in macroeconomic models, owing to its characteristic of determining the difference in the time, rather than the level, of the accumulation rate (investment per capital stock). Futagami (Matsuyama Syôdai Ronsyû (Matsuyama Univ Commer Rev) 39(5–6):1–7, 1989) is the only study that attempted to establish a microfoundation for this function, but not within the typical framework of mainstream economics. Matsuo (Sei Hôsoku Taikê (Say’s law system), Chap. 5. Kyushu University Press, Fukuoka, 1992) and Ishiguro (Rokkodai Ronshu, Kobe Univ 38(3):68–80, 1991; Shokei-Gakuso (J Bus Econ), Kinki Univ 42(2–3):205–212, 1995) introduced regressive expectations into the conventional model of dynamic maximisation of the sum of the present value of net cash flow using the Uzawa–Penrose adjustment cost function of investment, but they derived functions that determine the level of the accumulation rate. In this study, we introduce the new adjustment cost function of investment suggested by Eguchi (Dôgakuteki ippan kinkô moderu ni yoru zaisê sêsaku no bunseki (Analysis of fiscal policy in dynamic general equilibrium model). Mitsubishi Economic Research Institute, 2011), Hayashida et al. (Jpn Polit Econ 48(1):67–86, 2022), and Yasuoka et al. (AK type production function in DSGE model. Kuansei Gakuin University School of Economics Discussion Paper 246, 2023) into Matsuo’s (1992) framework and successfully derive the Harrod–Okishio investment function using the variational method.