Humans have created highly developed cultures, brought about by iterative improvements in technology. Using a mathematical model, I investigated the conditions under which cultural traits tend to be improved for a higher level of culture to evolve. In the model, I consider three ways of learning: individual learning, simple social learning, and improvements of socially learned cultural traits (social improvement). I obtain the evolutionarily stable number of cultural traits acquired through each way of learning. I show that organisms improve many socially learned cultural traits under the following conditions: (1) environmental stability is intermediate; (2) the environment is severe; (3) the success rate of individual learning is high; (4) the utility of cultural traits acquired by individual learning is large; (5) the accuracy of social learning is high; and (6) the increase in the utility of beneficial cultural traits attained by social improvement is large. I also show that when organisms have greater ability for social improvement, the average utility of the beneficial cultural trait increases, the proportion of beneficial cultural traits among all cultural traits decreases, and the total number of cultural traits acquired by the three ways of learning is constant. These results shed light on the origins of human cumulative culture.