Sprawl and low urban density are often considered challenges to the vitality and efficiency of metropolitan areas. Utilizing a difference equation approach to endogenize density choices, this paper examines how competition between new cities causes development to occur too quickly compared to welfare maximizing development. Early development causes land to be sold in larger lots to a smaller number of buyers, causing lower population density. Competition in a timing game among developers causes early development, lower population density and lower capital density.
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