Thread: calculus question about maximization

hi, I could not solve this question and need your help.
http://i49.tinypic.com/35bh6d1.jpg

Hey umit.

For this you need to first find V.

It says in this question that everybody can vote, but it also only mentions five people (the two ministers and the other three people). If this is the only population in Coco, then it means that U = 3 and V = 0 since P = 2 and U^2 = 3^2 which means P - U^2 = 2 - 3^2 = -7 < 0 so V will always equal zero.

Under these assumptions, no government will ever win the election since no government will ever have fifty percent of the votes.

Now in order for any government to get fifty percent of the votes they will need to get V > 50% of the the population which consists of U + P where P are the number of employed people and U are the number of unemployed people.

So we need V > 0.5(U + P) and V = P - U^2 so P - U^2 > 0.5(P + U) or P - U^2 > 0.5U + 0.5P so 0.5P > U^2 + 0.5U or P > 2U^2 + U.

When this is the case, the government has a chance of winning the election only when the number of employed people P is greater than 2U^2 + U where U is the number of unemployed people.

Thank you so much for your help