When it spends money on education a government is trying to

... meet a social need and improve the economy.

The government sponsors education because it contributes to the good of society and the economy.  The United States Department of Education has been a Cabinet-level department of the federal government since 1980.  There is some talk in the present administration about combining the Department of Education with the Department of Labor -- which indicates that the government does see a connection between education and the economy (labor, jobs). 

The Department of Education budget approved for the current fiscal year is set at just under 71 billion dollars, which was $2.6 billion dollars higher than the previous year's Education budget.  And that's just what is spent on the federal level.  Most education costs are paid by local governments through property taxes, as well as supported by state budgets.  From the municipal to the national level, education remains a spending priority for government leaders.