In this paper I present a methodology to calculate the benefits of in-kind programs such as public housing which restrict consumption of some goods to the levels offered by the government. Most previous studies begin with an a priori specification of the direct utility function. I begin with the ordinary demand function and then integrate demand to recover the indirect utility function and the expenditure function. I argue that this approach gives additional flexibility in choosing a functional form which best describes the data. I then use this methodology to estimate the benefits of the U.S. government's Section 8 housing program.