American Institute of Mathematical Sciences

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2015, 5(3): 233-236. doi: 10.3934/naco.2015.5.233

Pseudoconvexity properties of average cost functions

R. Enkhbat 1, , N. Tungalag 2, and  A. S. Strekalovsky 3,

1. 

The School of Business, National University of Mongolia, P.O.BOX-46/635, Ulaanbaatar 210646, Mongolia
2. 

The School of Business, National University of Mongolia, Ulaanbaatar 210646, Mongolia
3. 

Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Russian Federation

Received  October 2014 Revised  June 2015 Published  August 2015

It is well known that short run cost functions of firms are convex functions when production functions are concave [14]. Average cost minimization as a classical economics problem has been studied in fundamental textbooks [14,4,7,8] and in the literature [2,3,9,12,13,1]. However, it seems that less attention so far has been paid to the study of properties of the average cost function and its minimization methods. The aim of this paper is to fulfill this gap. First, we show that average cost functions are pseudoconvex. Second, we develop an algorithm for solving the average cost minimization problem. We implement the algorithm to solve a real carpet manufacturing problem in Mongolia.
Keywords: cost minimization, local and global minimizers, pseudoconvexity, Mathematical economics, average cost..
Mathematics Subject Classification: Primary: 49M, 49.
Citation: R. Enkhbat , N. Tungalag, A. S. Strekalovsky. Pseudoconvexity properties of average cost functions. Numerical Algebra, Control and Optimization, 2015, 5 (3) : 233-236. doi: 10.3934/naco.2015.5.233
References:
[1]

A. Adriana and L. Tony, Cost minimization under variable input prices: A theoretical approach, Romanian Journal for Economic Forecasting, 1 (2013), 70-86.

[2]

L. Basskin, Using cost-minimization analysis to select from equally effective alternatives, Formulary, 33 (1998), 1209-1214.

[3]

A. H. Briggs and B. J. O'Brien, The death of cost-minimization analysis? Health Economics, 10 (2001), 179-184.

[4]

Donald W. Katzner, Walrasian Microeconomics: An Introduction to the Economic Theory of Market Behavior, Addison-Publisher, 1988.

[5]

R. Enkhbat, Quasiconvex Programming, Lambert Publisher, Germany, 2009.

[6]

R. Enkhbat, Y. Bazarsad and J. Enkhbayar, A method for fractional programming, International Journal of Pure and Applied Mathematics, 73 (2011), 93-99.

[7]

J. Henderson and R. Quandt, Microeconomic Theory: A Mathematical Approach, McGraw-Hill Book Company, 1980.

[8]

M. D. Intriligator, Mathematical Optimization and Economic Theory, SIAM, 2002 doi: 10.1137/1.9780898719215.

[9]

M. Mahmud Khan, D. Ali, Z. Ferdousy and A. Ali-Mamun, A cost-minimization approach to planning the geographical distribution of health facilites, Oxford Journals, Medicine, Health Policy and Planning, 16 (2001), 264-272.

[10]

O. L. Mangasarian, Pseudo-Convex Functions, Journal of the Society for Industrial and Applied Mathematics Series A, 3 (1965), 281-290.

[11]

S. K. Mishra, K. K. Lai and S. Wong, Generalized Convexity and Vector Optimization, Springer, 2009.

[12]

D. Newby and S. Hill, Use of pharmacoeconomics in prescribing research. Part 2: Cost minimization analysis-when are two therapies equal? Journal of Clinical Pharmacy and Therapeutics, 28 (2003), 145-150.

[13]

C. Rose and R. Yates, Minimizing the average cost of paging under delay constraints, Wireless Networks, 1 (1995), 211-219.

[14]

A. Takayama, Analytical Methods in Economics, Harvester Wheatsheaf, 1994.

show all references

References:
[1]

A. Adriana and L. Tony, Cost minimization under variable input prices: A theoretical approach, Romanian Journal for Economic Forecasting, 1 (2013), 70-86.

[2]

L. Basskin, Using cost-minimization analysis to select from equally effective alternatives, Formulary, 33 (1998), 1209-1214.

[3]

A. H. Briggs and B. J. O'Brien, The death of cost-minimization analysis? Health Economics, 10 (2001), 179-184.

[4]

Donald W. Katzner, Walrasian Microeconomics: An Introduction to the Economic Theory of Market Behavior, Addison-Publisher, 1988.

[5]

R. Enkhbat, Quasiconvex Programming, Lambert Publisher, Germany, 2009.

[6]

R. Enkhbat, Y. Bazarsad and J. Enkhbayar, A method for fractional programming, International Journal of Pure and Applied Mathematics, 73 (2011), 93-99.

[7]

J. Henderson and R. Quandt, Microeconomic Theory: A Mathematical Approach, McGraw-Hill Book Company, 1980.

[8]

M. D. Intriligator, Mathematical Optimization and Economic Theory, SIAM, 2002 doi: 10.1137/1.9780898719215.

[9]

M. Mahmud Khan, D. Ali, Z. Ferdousy and A. Ali-Mamun, A cost-minimization approach to planning the geographical distribution of health facilites, Oxford Journals, Medicine, Health Policy and Planning, 16 (2001), 264-272.

[10]

O. L. Mangasarian, Pseudo-Convex Functions, Journal of the Society for Industrial and Applied Mathematics Series A, 3 (1965), 281-290.

[11]

S. K. Mishra, K. K. Lai and S. Wong, Generalized Convexity and Vector Optimization, Springer, 2009.

[12]

D. Newby and S. Hill, Use of pharmacoeconomics in prescribing research. Part 2: Cost minimization analysis-when are two therapies equal? Journal of Clinical Pharmacy and Therapeutics, 28 (2003), 145-150.

[13]

C. Rose and R. Yates, Minimizing the average cost of paging under delay constraints, Wireless Networks, 1 (1995), 211-219.

[14]

A. Takayama, Analytical Methods in Economics, Harvester Wheatsheaf, 1994.

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