The Model Of Directed Technical Change With Endogenous Skill Supply

This paper builds an endogenous directed technical change model with human capital investment decision which endogenous labor wage has been taken into account in the decision and the absolute amount of the wage of skilled workers has been calculated to research the endogenous supply of skilled-workers in the economy and the structure of the human capital,and to discuss the structure of human capital and the skill premium under different substitution elasticity of product.Firstly,the theoretical part constructs an endogenous directed technical change model with individual human capital investment decision.By modeling individual’s utility function,labor’s credit market and individual human capital investment decision and solving the equilibrium,it is concluded that the supply of skilled labor depends on the wage of skilled-workers and the cost of education.Secondly,by modelling production department,technology monopoly department and research and development department and solving the equilibrium,the absolute amount of endogenous wage of skilled workers is calculated and analyzed.After obtaining the endogenous determination of the absolute amount of labor wage,the theoretical result of the endogenous determination of the supply of skilled labor can be acquired.Thirdly,based on the analysis of the sector of labors and the sector of producers,the theoretical results of the supply of endogenous skilled-workers and the absolute wage of endogenous skilled-workers can be obtained,thus solving the two specific problems of endogenous structure of human capital and endogenous wage of labors at the same time.Finally,numerical calculation method is adopted,and Matlab software is used to assign values to the parameters in the model,and the initial wealth distribution of individuals consistent with the real world is given.The theoretical results are visually displayed,which also verifies the feasibility and explanatory power of the modelBased on theoretical model derivation and numerical calculation,this paper draws the following conclusions:(1)Both labor wage and the cost of education will affect individual human capital decisions.(2)With the increase of the cost of education,the number of skilled workers decreases while the number of unskilled workers increases under the conditions of skill-biased technical change,skill-neutrality technical change and skill-substitution technical change,and the wage gap between skilled labor and unskilled labor decreases.(3)The difference in the elasticity of substitution of intermediate products leads to the different effects of the cost of education and human capital structure on the skill premium.(4)The increased elasticity of substitution of intermediate products will increase the number of skilled labor force in the economy and reduce the number of unskilled labor force.Through the study of the above theoretical model and the analysis of numerical results,this paper can explore the differences between the final con vergence states caused by the different initial states in different economic systems.The practical significance of this paper lies in that if the initial cost of education is low,the number of skilled workers in the economy will be large under the condition that the total labor force is fixed.If not,the opposite is true.Therefore,the government can improve individuals’ willingness to receive education by providing educational subsidies to individuals,thus increasing the scale of skilled labor force.The model can also be used to study the optimal human capital structure corresponding to the optimal economic growth rate and the digital economy and big data can be introduced into the endogenous directed technical change model.