A Housing Supply Absorption Rate Equation

Abstract

What is the optimal rate of new housing supply? We answer this question with a simple model of new housing supply where the choice variable is the rate of new housing lot sales. This model is informed by the cost-side assumptions of the static equilibrium model but allows for demand for home-buying to vary over time. It differs from static models of housing production equilibrium by assuming that landowners hold land assets that are sold in asset markets to create new supply. Landowners maximise the present value of their balance sheet by choosing a rate of new housing lot sales, accounting for the effect on asset price growth from their sales in a housing market of finite depth. The resulting absorption rate equation has radically different parameter effects compared to the popular static housing density model. Constraints on density, for example, increase the optimal rate of supply by reducing the return to delaying development. Interest rates, land value tax rates, and demand growth, positively relate to the optimal rate of supply. The policy lessons are (1) the relationship between demand growth and the optimal supply rate limits the ability for market supply to reduce prices, and (2) increasing the cost to delaying housing development is the primary way to increase the market rate of housing supply.