טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTaly Harel
SubjectA Computational Approach to Duopoly Equilibrium with Capital
and R and D Investments: Application to the AOI
Industry
DepartmentDepartment of Industrial Engineering and Management
Supervisor Full Professor Abraham Subotnik


Abstract

This research describes a method for computing equilibrium over time for a duopolistic industry where competing firms decide on a number of different investments. These decisions take into consideration the competitors’ actions, where these decisions have long-term influence upon the firm itself and upon the competitors. This thesis examines the applicability of the numeric solution method (non linear) in finding a dynamic equilibrium for an industry characterized by a strategic dependence between the participants, with special emphasis on R&D investments.

These investments in R&D are associated with an external component such as technological spillovers, which complicate the computation of the optimal R&D strategy of the firm and the characteristic of the equilibrium of the industry.

In order to compute the equilibrium of this industry by the MATLAB software, we are required to define the size of the grid from which the investment rates can be chosen. We are also required to define parameters and initial values on which the computations will be performed.

The optimal strategies that were generated by the solutions of the model ovet time are: Orbotech - total investment of 70% out of cash flow, allocated to 40% in R&D and 60% in marketing investment; Camtek - total investment of 30% out of cash flow, allocated to 30% in R&D, 60% in marketing investments and 10% in physical capital. The stability of the equilibrium results was checked by sensativity the calibration process.

The thesis also examines two alternatives of governmental policy: first, subsidizing R&D expenses of the firms and second, a decrease of the companies tax rates. These alternatives are evaluated at the firm’s level and on social welfare .