Katja produces potato Her production function is QL A 6L 02

Katja produces potato. Her production function is Q(L, A) = 6L 0,25A, where L denotes labour, while A denotes land. Calculate the marginal rate of technical substitution of land in the point: (A=2, L=4)!

Solution

Katja has a production function Q(L, A) = 6L^(0.25)A, where L denotes labour, while A denotes land.

The marginal rate of technical substitution of land for labor is given by = MPL/MPA

MPL = 6*(0.25)*(L^(-0.75))*(A^0.5) and MPA = 6*0.5*(L^0.25)*(A^(-0.5)).

Simplification of these expressions give the MRTS

= A/2L

When we have a point (A=2, L=4), MRTS = 2/2*4 = 1/4 or 0.25.