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 & 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.   Google Scholar

[2]

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

[3]

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

[4]

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

[5]

R. Enkhbat, Quasiconvex Programming,, Lambert Publisher, (2009).   Google Scholar

[6]

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

[7]

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

[8]

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

[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, 16 (2001), 264.   Google Scholar

[10]

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

[11]

S. K. Mishra, K. K. Lai and S. Wong, Generalized Convexity and Vector Optimization,, Springer, (2009).   Google Scholar

[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.   Google Scholar

[13]

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

[14]

A. Takayama, Analytical Methods in Economics,, Harvester Wheatsheaf, (1994).   Google Scholar

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.   Google Scholar

[2]

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

[3]

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

[4]

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

[5]

R. Enkhbat, Quasiconvex Programming,, Lambert Publisher, (2009).   Google Scholar

[6]

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

[7]

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

[8]

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

[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, 16 (2001), 264.   Google Scholar

[10]

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

[11]

S. K. Mishra, K. K. Lai and S. Wong, Generalized Convexity and Vector Optimization,, Springer, (2009).   Google Scholar

[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.   Google Scholar

[13]

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

[14]

A. Takayama, Analytical Methods in Economics,, Harvester Wheatsheaf, (1994).   Google Scholar

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