Quiz 4

Q: If f(L,K)=L^{.5}K^{.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^{.5}K^{.5} =30.

Combing these two we have 30=(25K)^{.5}K^{.5 }or30=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.