# Math Help - Marginal products of labor and capital

1. ## Marginal products of labor and capital

Hey,

has anybody an idea how to compute of marginal products of labor and capital from this excercise?

2. ## Re: Marginal products of labor and capital

post the whole question.

Hint: consider three cases:
1) aK < bL
2) aK > bL
3) aK=bL

and find the marginal capital in each.

3. ## Re: Marginal products of labor and capital

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?

4. ## Re: Marginal products of labor and capital

i dont think thats right.

case 1: aK < bL
$Y = min(aK,bL)^a \rightarrow Y = (aK)^a$

MPL=0.

case 1: aK > bL
$Y = min(aK,bL)^a \rightarrow Y = (bL)^a$

$MPL =abL^{a-1}$

case 3: aK=bL
MPL=0

So the overall MPL function is $abL^{a-1}$ if bL < aK, 0 otherwise.