Britain’s new leader, Andy Burnham, is facing the same old problem: How can he kickstart a sluggish economy so that growing companies and increased output generate enough additional revenue to boost defense spending and pay for everything else voters want without raising taxes? It’s a question that has bedeviled every prime minister since the financial crisis of 2008. And their failure to find an answer is a big part of the reason that the men and women who have taken up residence behind the famous black door at 10 Downing Street in that period have had an average tenure of two years.