# Partially increasing a variable

1. Mar 30, 2008

### brollysan

1. The problem statement, all variables and given/known data

Given the utility function u(x1,x2)= (x1)^a + (x2)^a where 0<a<1

Find the marginal substitution rate

Find the change in the marginal substitution rate when x2 is partially increased.

2. Relevant equations

Marginal rate of substitution: dx2/dx1= -(du(x1,x2)/dx1)/(du(x1,x2)/dx2

3. The attempt at a solution

By partially derivating i get that the marginal rate of substituion (MRS) is -(ax1^(a-1))/ax2^(a-1)

When x2 is partially increased, does it simply mean i add a constant to x2?