This paper investigates a representative landlord's profit-maximization problem in a stationary economy. The landlord must decide on the quality of his housing units at the time of construction, maintenance expenditure over the life of the building, and the time of demolition or rehabilitation. The analysis can be applied to other problems with similar economic structure, notably equipment and durable good maintenance, overhaul and replacement.

The paper considers the problem of statistical inference with estimated Lorenz curves and income shares. The full variance-covariance structure of the (asymptotic) normal distribution of a vector of Lorenz curve ordinates is derived and shown to depend only on conditional first and second moments that can be estimated consistently without prior specification of the population density underlying the sample data. Lorenz curves and income shares can thus be used as tools for statistical inference instead of simply as descriptive statistics.