Under representative democracy, representatives are elected across a polity and assemble under one roof in a political center. A fundamental concern to the functioning of representative democracy is therefore 'the problem of space', i.e., the geographical inequality of access to political representation: How can peripherally and centrally residing MPs have equitable access to representing their constituents in parliament? Existing research documents that geographic inequality in representation is prevalent in rich democracies, and that voters prefer candidates with local ties. However, the representational effects of this inequality remain unclear. We remedy this gap, studying the geographical representation and behavior of Danish MPs from 1990--2022 with a novel data set linking MP residence and other characteristics to parliamentary behavior. For causal identification we exploit a series of reforms that jointly dramatically lowered commuting costs specifically for peripheral candidates, namely i) the opening of the Great Belt Bridge, which reduced travel time to parliament, ii) the introduction of a dual residence allowance, and iii) the provision of a free MP apartment close to parliament. We study the effects of these reforms on representational behavior for geographically peripheral vs. central MPs. Our results have implications for how to promote and sustain geographical equality in representation.