Hey,
has anybody an idea how to compute of marginal products of labor and capital from this excercise?
- [min{aK,bL}]^α
The whole question is :
Compute marginal products of labor and capital and the marginal rate of technical substitution and sketch the isoquants for the following production function: [min{aK,bL}]^α
marginal products of labor: α[min{aK,bL}]^α-1*(0, if L>K; b if L<K)? is it correct?
i dont think thats right.
case 1: aK < bL
$\displaystyle Y = min(aK,bL)^a \rightarrow Y = (aK)^a$
MPL=0.
case 1: aK > bL
$\displaystyle Y = min(aK,bL)^a \rightarrow Y = (bL)^a$
$\displaystyle MPL =abL^{a-1}$
case 3: aK=bL
MPL=0
So the overall MPL function is $\displaystyle abL^{a-1} $ if bL < aK, 0 otherwise.