Quiz 4 Q

Quiz 4
Q: If f(L,K)=L^.5K^.5, w=1, and v=25, what is the cheapest cost of producing 30 units of out put?

A: First, we need two equations to find the optimal input bundle.
    Use RTS=w/v, which is K/L=1/25 or 25K=L.
    Also, use L^.5K^.5 =30.

    Combing these two we have 30=(25K)^.5K^.5or30=5K.
    Therefore, K=6 and hence L=25(6)=150.
    Hence the minimum cost of making q=30 units of output is 1(150)+25(6)=150+150=300.