Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change

Economic growth is a function of the interactions between the different productive factors framed in the economic policy of an economy, in particular, it can be expressed in terms of labour force, productive resources (land, capital) and technology, among others. The present work pretends to approximate a model to explain the economic growth in developing economies, for which a model is proposed that explains this growth in function of the referred factors; then production is proposed in function of capital and work and two models are adjusted, one with exogenous technological change and the other that involves technological change in an endogenous manner. The model is developed with a production function with constant substitution elasticity so that it is applicable to both developed and developing economies, since it is to be expected that in developed economies the substitution elasticity is unitary, which would lead to a Cobb-Douglas-type production function, but it is very probable that in incipient economies the function with constant substitution elasticity better reflects the relationship between production factors and economic growth. The research allows the development of the corresponding mathematical model in each case, the economic and mathematical foundations of each model are presented and validated according to economic theories. The behaviour of variables such as savings, investment, income, consumption, capital and their relationships in each model is analysed.