Price elasticity studies analyze how customers react to price changes. In this paper, we focus on their effect on the renewal of non-life insurance contracts. Every year insurers face the recurring question of adjusting premiums. Where is the trade off between increasing premium to favour higher projected profit margins and decreasing premiums to obtain a greater market share? Regression models are used to explore the triangular relationship of the customer, the insurer and the market. We conclude that the latter cannot be ignored if we want to get reliable lapse predictions. Furthermore, we also investigate empirical evidence of adverse selection and study its potential impact on lapse decisions.