Non-convex aggregate technology and optimal economic growth

Abstract

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state equilibrium toward which the convergence of the optimal paths is monotone and asymptotic. When the discount rate is in some intermediate range, we …nd su¢ -cient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, the optimal paths converge to one single appropriate equilibrium steady state. This state might be a poverty trap with low per capita capital, which acts as the extinction state encountered in earlier studies focused on S-shapes production functions. Second, we consider the case of linear utility and provide su¢ cient conditions to have either unique or two steady states when the discount rate is in some intermediate range . In the latter case, we give conditions under which the above critical value might not exist, N.M. Hung and C. Le Van thank the referee for very helpful remarks and criticisms. They are grateful to Takashi Kamihigashi for very fruitful discussions.y ( Corresponding author )

Monotonicity and continuity of the critical capital stock in the Dechert–Nishimura model

“…This threshold property is often associated with important economic phenomena such as history dependence and poverty traps. Dechert and Nishimura's (1983) analysis has been extended by various studies on optimal growth with nonconvexities (e.g., Majumdar and Mitra, 1982;Majumdar and Nermuth, 1982;Mitra and Ray, 1984;Kamihigashi and Roy, 2007;Hung et al, 2009). The threshold property described above is also widespread even outside the optimal growth literature, arising in a broad range of economic problems concerning, for example, optimal investment for firms (e.g, Hartl and Kort, 2004;Haunschmied, et al, 2005;Wagener, 2005), renewable resources (e.g., Wirl, 2004), political behavior (e.g, Caulkins et al, 2007), and drug control (Tragler et al, 2001;Levy et al, 2006).…”

Economic growth, poverty traps and cycles: productive capacities versus inefficiencies

“…Indeed, in order to analyse equilibria and cycles in economic growth, previous literature shows that a model must assume a concave-convex production function (Skiba, 1978; Askenazy and Le Van, 1999; Hung et al ., 2009). In this line, in what follows we model an augmented convex-concave production function to analyse and understand the impact on growth dynamics of productive capacity (capacity utilization) and technological inefficiencies.…”

Cumulative scheduling with variable task profiles and concave piecewise linear processing rate functions

“…In [12], the authors use linear functions to approximate real-world ones. Despite the fact that there exist many real-world processing functions, which are concave [8,11], approximating a function by a concave piecewise linear one is always at least as good as an approximation by a linear function (see Example 2 below). Furthermore, the authors of [12] prove the NP-hardness of their problem using a reduction from the cumulative problem.…”