Abstract In this paper, we investigate a four-dimensional dynamic nonlinear model inspired by Kaleckian theory that was developed by Murakami and Asada. The model describes the dynamics of the utilization rate, wage share, nominal interest rate, and expected inflation rate. We analyze the impact of the model's parameters on the qualitative properties of solutions in the neighbourhood of its equilibrium, with particular emphasis on equilibrium stability and the existence of business cycles. Our results prove that specific parameter values can induce business cycles. The methodology employed to establish this finding is based on Hopf bifurcation theory and the theory of normal forms of dynamic systems. The qualitative characteristics of the arising business cycles are determined by the bifurcation equation of the model, the construction of which is detailed in this study. Numerical simulations illustrate the impact of the parameter expressing the speed of revisions in inflation–deflation expectations on the qualitative properties of the corresponding business cycles for selected values of model parameters. This approach also offers insights into how other model parameters influence the qualitative properties of solutions. The insights gained from this study can be utilized by monetary and fiscal policy managers to regulate the economy with the aim of achieving sustainable growth.

Abstract Given the growing importance of measuring both the degree and sources of resilience following major shocks, the concept of resilience has attracted increasing scholarly attention. However, no universally accepted measurement exists, and prevailing approaches offer limited insight into industrial impacts. This study provides a structural sensitivity index to measure the industrial sources of regional employment resilience and applies it to the Japanese economy between 1980 and 2012. We present a novel formula that quantifies the sources of regional resilience through within-sector and structural change effects and reveals how unevenly different local industries contribute to regional resilience. A chronological and geographical exploration of employment resilience shows that Japanese prefectures gradually became more resilient after the 1990s, accompanied by rising regional heterogeneity. Furthermore, the structural change effect consistently undermines regional resilience, whereas regional resilience benefits from favourable within-sector effects. Finally, the increase in regional heterogeneity behind improvements in resilience is accompanied by industrial unevenness from different time horizons. However, the relationship between industrial unevenness and resilience is not spatially uniform, suggesting that regional context plays a critical role in shaping resilience outcomes.

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.

Based on the studies of Okishio and Roemer, this study discusses the relationship between surplus value and technological change that reduces costs and labor value by industry. Previous studies were limited in that they constructed a one-country model using a single wage rate and did not consider imported intermediate goods. Therefore, we extend the framework of the previous studies to a case in which imported intermediate goods exist and wage rates differ across countries, using a two-country, two-sector model and a multicountry-multisector model in this study. The analysis reveals that when surplus labor is negative in a country that imports intermediate goods, technological change occurs that reduces costs but uses more direct and indirect labor in the country’s industries. The type of technological change was found to be capital-using and labor-saving.