Marginal product and technical rate of substitution?

Question

please please help me. for these complements

f(x1, x2) = min {2(x1), 3(x2)}

how do i find marginal product1 and marginal product2??

and then how do i find MRTS?

i asked my teacher and she said you do one case for each, holding other just as MP2 or MP1... for MRTS

but i don't get it, i'm not sure if i understand this...!!

Answer 1

You'll take the derivative of f wrt to each. In this case:

MP1= 2  for X1< 3/2 X2    and  MP1=0  for X1 > 3/2 X2

MP2= 3  for X2 < 2/3 X1   and MP2 =0 for X2 > 2/3 X1

MRTS is the trade off between the inputs OR put another way the ratio of MPs  clearly you are using one or the other not both