Partial Differentiation - Marginal Rate of Technical Substitution

[mroberts]

Hi

I cant equate my calculation for the Marginal Rate of Technical Substitution to the partial derivatives I have done on the production function.

I am trying to equate the MRTS figures in the table to my partial derivatives below.

Y=X1^0.1.X2^0.4
dY/dX1 = 0.1X1^-0.9.X2^0.4
dY/dX2 = 0.4X1^0.1.X2^-0.6
MRTS = 1/4*X2/X1
MRTS=X2/(4.X1)

How do I obtain the figure of 50.313 from the table using MRTS = X2/4X1 ?

Thanks for any help!

 

[Ishuda]

Hi

I cant equate my calculation for the Marginal Rate of Technical Substitution to the partial derivatives I have done on the production function.

I am trying to equate the MRTS figures in the table to my partial derivatives below.

Y=X1^0.1.X2^0.4
dY/dX1 = 0.1X1^-0.9.X2^0.4
dY/dX2 = 0.4X1^0.1.X2^-0.6
MRTS = 1/4*X2/X1
MRTS=X2/(4.X1)

How do I obtain the figure of 50.313 from the table using MRTS = X2/4X1 ?

Thanks for any help!

You don't. Notice that in the table, Y is constant so that you essentially have
X2 = 316.228 X1^-0.25
So what is the derivative of X2 wrt X1 and what would be n approximation to that derivative?