RDP 2001-08: City Sizes, Housing Costs, and Wealth Equation (A6)

h_{i} = \frac{\int_{0}^{R} h (r) 2 π r d r}{π R^{2}} = \frac{ψ \int_{0}^{P_{i}} \sqrt{P_{i} - a} d a}{P_{i} \sqrt{π}} = \frac{ψ \sqrt{P_{i}}}{3 \sqrt{π}}