scholarly journals On the uniqueness of the solution of the cost minimization problem with generalized Sato production function

2021 ◽  
Vol 12 (1) ◽  
pp. 37-48
Author(s):  
Vedran Kojic ◽  
Zrinka Lukac ◽  
Krunoslav Puljic

Whenever a firm is maximizing its profit, it necessarily has to minimize its cost. Thus, the cost minimization problem is one of the central problems in the theory of the firm. When presenting this problem, the majority of microeconomic textbooks use very well-known production functions, such as Leontief, Cobb-Douglas, or other CES production functions. The goal of this paper is to analyze the cost minimization problem with the generalized Sato production function. The generalized Sato production function is one of the non-standard production functions with variable elasticity of substitution. First, we show that the generalized Sato production function is continuous, strictly monotone, strictly quasiconcave and that a positive amount of output requires positive amounts of some of the inputs. Next, by using mathematical programming we show that the cost minimization problem with generalized Sato production function has a unique solution. This result is very important since it implies the existence of the corresponding cost function and conditional input demands.

2021 ◽  
Author(s):  
Françoise Larbre

Depending on the workers qualification, the use of robots is perceived either as a helpful tool or as a competitor. We analyze the substitution of capital for labor, including the case where the product is entirely made by robots. We use CES production functions and their derived cost functions (the later being surprisingly missing in the literature). We focus on short-run and the case of an elasticity of substitution greater than 1. We highlight a level of product for which the cost is identical regardless of the factor used. As a joint product, we provide a foundation to cost functions exhibiting first increasing and then decreasing returns to scale (a so far missing justification to the usually assumed shape of cost functions).


2022 ◽  
Vol 18 (2) ◽  
pp. 1-25
Author(s):  
Jing Li ◽  
Weifa Liang ◽  
Zichuan Xu ◽  
Xiaohua Jia ◽  
Wanlei Zhou

We are embracing an era of Internet of Things (IoT). The latency brought by unstable wireless networks caused by limited resources of IoT devices seriously impacts the quality of services of users, particularly the service delay they experienced. Mobile Edge Computing (MEC) technology provides promising solutions to delay-sensitive IoT applications, where cloudlets (edge servers) are co-located with wireless access points in the proximity of IoT devices. The service response latency for IoT applications can be significantly shortened due to that their data processing can be performed in a local MEC network. Meanwhile, most IoT applications usually impose Service Function Chain (SFC) enforcement on their data transmission, where each data packet from its source gateway of an IoT device to the destination (a cloudlet) of the IoT application must pass through each Virtual Network Function (VNF) in the SFC in an MEC network. However, little attention has been paid on such a service provisioning of multi-source IoT applications in an MEC network with SFC enforcement. In this article, we study service provisioning in an MEC network for multi-source IoT applications with SFC requirements and aiming at minimizing the cost of such service provisioning, where each IoT application has multiple data streams from different sources to be uploaded to a location (cloudlet) in the MEC network for aggregation, processing, and storage purposes. To this end, we first formulate two novel optimization problems: the cost minimization problem of service provisioning for a single multi-source IoT application, and the service provisioning problem for a set of multi-source IoT applications, respectively, and show that both problems are NP-hard. Second, we propose a service provisioning framework in the MEC network for multi-source IoT applications that consists of uploading stream data from multiple sources of the IoT application to the MEC network, data stream aggregation and routing through the VNF instance placement and sharing, and workload balancing among cloudlets. Third, we devise an efficient algorithm for the cost minimization problem built upon the proposed service provisioning framework, and further extend the solution for the service provisioning problem of a set of multi-source IoT applications. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms are promising.


2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Serena Brianzoni ◽  
Cristiana Mammana ◽  
Elisabetta Michetti

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.


1978 ◽  
Vol 3 (3) ◽  
pp. 209-231 ◽  
Author(s):  
Solomon W. Polachek ◽  
Thomas J. Kniesner ◽  
Henrick J. Harwood

This research examines scholastic performance within the context of an individual’s production function. A constant partial elasticity of substitution production function for academic achievement is presented and estimated with non linear maximum likelihood methods. We find that ability and time devoted to various aspects of the learning process are the most important determinants of students’ accomplishments. Our results underscore the potential for students to compensate for relatively “poor” educational backgrounds by spending more time on study and class attendance.


2003 ◽  
Vol 7 (4) ◽  
pp. 207-228 ◽  
Author(s):  
Hrvoje Podnar ◽  
Jadranka Skorin-Kapov

We present a genetic algorithm for heuristically solving a cost minimization problem applied to communication networks with threshold based discounting. The network model assumes that every two nodes can communicate and offers incentives to combine flow from different sources. Namely, there is a prescribed threshold on every link, and if the total flow on a link is greater than the threshold, the cost of this flow is discounted by a factor α. A heuristic algorithm based on genetic strategy is developed and applied to a benchmark set of problems. The results are compared with former branch and bound results using the CPLEX® solver. For larger data instances we were able to obtain improved solutions using less CPU time, confirming the effectiveness of our heuristic approach.


2008 ◽  
Vol 12 (5) ◽  
pp. 694-701 ◽  
Author(s):  
Hideki Nakamura ◽  
Masakatsu Nakamura

We consider endogenous changes of inputs from labor to capital in the production of intermediate goods, i.e., a form of mechanization. We derive complementary relationships between capital accumulation and mechanization by assuming a Cobb–Douglas production function for the production of final goods from intermediate goods. A constant-elasticity-of-substitution production function in which the elasticity of substitution exceeds unity can be endogenously derived as the envelope of Cobb–Douglas production functions when the efficiency of inputs is assumed in a specific form. The difficulty of mechanization represents the elasticity of substitution.


2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Bang Wang ◽  
Qiao Kong ◽  
Qiang Yang

The ever increasing data demand has led to the significant increase of energy consumption in cellular mobile networks. Recent advancements in heterogeneous cellular networks and green energy supplied base stations provide promising solutions for cellular communications industry. In this article, we first review the motivations and challenges as well as approaches to address the energy cost minimization problem for such green heterogeneous networks. Owing to the diversities of mobile traffic and renewable energy, the energy cost minimization problem involves both temporal and spatial optimization of resource allocation. We next present a new solution to illustrate how to combine the optimization of the temporal green energy allocation and spatial mobile traffic distribution. The whole optimization problem is decomposed into four subproblems, and correspondingly our proposed solution is divided into four parts: energy consumption estimation, green energy allocation, user association, and green energy reallocation. Simulation results demonstrate that our proposed algorithm can significantly reduce the total energy cost.


2011 ◽  
Vol 214 (3) ◽  
pp. 501-511 ◽  
Author(s):  
Chan Hou Che ◽  
Weili Huang ◽  
Andrew Lim ◽  
Wenbin Zhu

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