Xavier and Yvette Are the Only Two Persons on a Desert

Multiple Choice

Xavier and Yvette are the only two persons on a desert island.There are only two goods, nuts and berries.Xavier's utility function is U(N_x, B_x) = N_xB_x.Yvette's utility function is U(N_y, B_y) = 5N_y + B_y.Xavier is endowed with 4 units of berries and 13 units of nuts.Yvette is endowed with 6 units of berries and 8 units of nuts.In a competitive equilibrium for this economy, how many units of berries does Xavier consume?

A) 37.50
B) 69
C) 34.50
D) 32.50
E) None of the above.