Applications of differential geometry in economic fields

This study is constructed in six chapters. In chapter one, it is expressed a historical analysis of production functions and works found on geometric properties of the production functions. Some fundamental definitions and theorems used in thesis are also given. In chapter two, theory of production and the properties of production functions are investigated. In chapter three, it is stated quasi-sum production functions. Besides, the results obtained for quasi-sum production functions satisfying the property CES are reconsidered. Chapter four and chapter five form the original part of thesis. In chapter four, the homothetic production functions are classified by using Allen determinants. It is proved that the Allen's matrices of Cobb-Douglas and ACMS production functions are always regular. Morever, several results are derived regarding the graphs of homothetic production functions. In chapter five, an Allen Determinant formula is obtained for the composite functions of the form f(x)=F(h_1(x_1 )×…×h_n(x_n)) and the composite functions completely are classified according to the formula. Some geometric results are also derived about graphs of composite functions. Besides, the notion of generalized composite function is introduced and a classification theorem is given for these kind functions. In chapter six, obtained results are evaluated and open problems proposed in this subject are presented.