This paper is aimed at developing a stochastic macroeconomic model useful to explain the effects of unexpected jumps in government spending per capita and in demographic variables on per capita economic growth. To do this, it is assumed that the stochastic dynamics of output and population are driven by mixed diffusion-jumps processes modulated by a Markov Chain. The most important results are that extreme sudden jumps in government spending per capita and in the population growth rate impact negatively the rate of per capita output growth. In particular, if there is a sudden sharp jump in the rate of population growth, then capital per capita suddenly decreases impacting negatively per capita output. Finally, the theoretical findings are supplemented with empirical evidence about the Mexican case obtained through a model that takes in account the volatility of the growth zrates of the population and the per capita public expense as well as the surprises in the jump intensities of both variables.