What are the consequences of government spending by imposing tax? The question is "If the government of country Z increases spending by \$12 million dollars and raises tax collections by the same amount, then what will be the overall impact of theses moves on real GDP in country Z." The official solution is that real GDP will increase by \$12 million because it is a balanced budget move.

However, I think it depends. Increased tax collection will discourage production while the spending would encourage production. Any suggestions will be appreciated.
Your professor want probably that you compute the keynesian multiplicator (hint: once you have the general formula, replace dT by dG and see what you get).

Intuition: if you raise G, you will raise your GDP. As Y increases, your consumption increases. But the taxes (T, lump sum) increase also, so the consumption decreases (it depends of the disposable income). The overall effect is a 1 to 1 increase of your GDP.