Question

when it spends money on education a government is trying to

Answer 1

When a government spends money on education they are trying to invest in the future. Much like a business invests in upgraded equipment, a government spending money on education is trying to make their citizens better so that the country can thrive in the future. This will help to increase the skilled labor and production capacity of the country.

Answer 2

... 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.