The ultimate goal of customer retention is to increase the profitability of companies. Reinartz, Thomas, and Kumar (2005) linked customer acquisition, relationship duration, and profitability using a probit two-stage lease squares model. In the simultaneous equation model, a probit model was used to capture the acquisition process and a Tobit model was used to estimate the relationship duration of acquired customers. In the profitability model, these authors included as explanatory variables the firm actions, customer actions, control variables, predicted acquisition probability, and predicted relationship duration. To account for the right-censoring, the authors used a standard right-censored Tobit model to estimate the profitability.
Besides stochastic methods, researchers have developed deterministic methods to capture the optimal retention spending to maximize profitability. Just as Blattberg and Deighton  determined the optimal level of acquisition spending, they asked managers similar questions about companies' past retention activities to draw the retention curve. The answers to these questions indicate the retention expenditure per prospect, $R, the retention rate obtained as a result of that expenditure, r, and the ceiling rate on the retention curve. The curve is assumed to be exponential and captured by the equation
where is a parameter ...