We explore the impact of regulatory and physical supply constraints on house price levels and volatility in England. We hypothesize that house prices react more strongly to changes in income in more constrained locations and test this proposition using a unique panel dataset of 353 local authorities, ranging from 1974 to 2008. We use a policy reform and historical density as instruments to identify the endogenous constraints-measures and document that both regulatory and physical constraints have a strong positive causal effect on the long-run impact of income on house prices. Our counterfactual analysis suggests that average house prices in England in 2008 would be 21.4 percent lower if the planning system were completely relaxed. The standard deviation of prices during the sample period would be 29.7 percent lower. House prices (volatility) would be 9.9 (13.1) percent lower absent of scarcity constraints and 2.8 (3.6) percent lower if England were totally flat. JEL classification: G12, R11, R21, R31, R52.