The "new urban economics" is rather explicit with respect to demand for housing but the supply of housing is usually treated in a very cursory fashion. Housing is normally regarded as a one-dimensional good and equilibrium in a city is mostly concerned with the land market rather than the housing market. This paper introduces, on the supply side, the concept of design parameters of a building and, on the demand side, the concept of housing attributes, i.e. multi-dimensional housing. By means of structural analysis an engineering cost function is obtained in terms of design parameters. Due to housing attributes, the demand for housing and the supply of housing, the latter being based on the engineering cost function, should be derived simultaneously. Equilibrium is defined on the housing market rather than on the land market. It is shown how in equilibrium housing rent, land rent design parameters on buildings, and population density all depend on distance from the center of the city and on parameters of the problem: income, city population, diameter of the city, and technical coefficients.