$1.$ With the data below for an economy last year, determine the economy$$s official unemployment rate. Clearly show your steps and calculations, including the economic factors involved.

Total population $=375\mathrm{.}35$ million.

Population under $16$ years old and or institutionalized $=62\mathrm{.}25$ million.

Retirees and stay$-$at$-$home parents $=18\mathrm{.}45$ million.

Unemployed full$-$time college students $=62\mathrm{.}78$ million.

Part$-$time workers looking for full$-$time jobs $=9\mathrm{.}16$ million.

Unemployed workers who are actively seeking jobs $=8\mathrm{.}55$million.

Unemployed workers who are not actively seeking jobs $=6\mathrm{.}15$ million.

$2.$ Discuss the impact of $($a$)$ cost$-$push inflation and $($b$)$ demand$-$pull inflation on an economy$$s real output and employment.