Ann works as a consultant in Washington, DC. She has preferences over goods x,y and z represented by the following utility function:

U(x,y,z)=1/3ln(x) + 1/3ln(y) + 1/3ln(z)

Suppose that she's endowed with e_x, e_y, e_z amount of these goods, and she faces prices p_x, p_y, p_z . Suppose that Ann's current wage is w^DC and that her labor supply is inelastic and equal to 1, l=1 (we assume she doesn't value leisure at all).

Find the total value of Ann's endowments if she sold them in DC, m. Consider a potential NYC wage offer of w^NYC=600 and calculate her utility level if she moved to NYC with that wealth level, m + w^NYC. Denote this utility level as u¹