If a government increases spending by $10 billion, could total GDP increase by more than $10?

it can increase more than 10 bn, less than 10 bn or even decrease. GDP = the value of the finished goods and services produced in an economy during a period of time, usually 1 year. so, assuming that in Y0 the GDP was 500 bn and government spending was 5 bn. In Y1 the government increase spending by 10 bn but the private sector increase by 10%. so in Y1 you will have a GDP of 495*1.1 = approx 544 bn + 10 bn = total of 554 bn