In 1987 we developed a model (de Jong and Cramer, 1987) for the simultaneous determination of private car ownership and mileage. This model lacks the explicit influence of fixed and variable costs. In the present model, which is a utility model, we introduce these costs through the budget restriction. The model allows for the ensuing non — convexity. We present Maximum Likelihood estimates, using data from the Dutch national budget survey of 1985, and some micro —simulation results.