A housing supply absorption rate equation

Abstract

What is the optimal rate of housing supply? We answer this question by creating a simple model of the optimal housing lot supply per period. The choice variable is how many lots to sell each period to maximise the value of the flow of economic returns over time. This model is informed by the optimal density result of the static equilibrium model but allows for demand to vary over time while accounting for own-supply effects on price growth. 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) that the influence of the price growth rate on supply limits the ability for market supply to reduce prices, and (2) that increasing the cost to delaying housing development is the primary way to increase the market rate of housing supply.