If the government believed that education should create equal opportunities for all members of society, they may wish to abolish private education in the UK. Some studies show that individuals with a private education background have more education, job and social opportunities than those who were educated by the state. Abolishing private education removes the differential bias of universities which tend towards those who are privately educated, creating more opportunities for those who were not to receive a private education in the first place, thus increasing their utility.
If you’d spent more than a year studying Economics without having heard of Adam Smith, I’d be surprised. The eighteenth-century Scottish economist and Oxford academic is often referred to as the ‘father of modern economics’ – his classic work, An Inquiry into the Nature and Causes of the Wealth of Nations, being considered the first contemporary publication of economics. His theories shaping the concepts of the free market and division of labour will unlikely be of news to current readers - however, prior to The Wealth of Nations being published in 1776, pre-Adamite economics was devoid of such principles. Although Smith saw vast success in his career, his life was not, as such, in parallel with his profession.