There are two consumers (A, B) with the following total utility functions (U) and endowments (W):

UA (XA1, XA2) = (lnXA1) + (1 - ) lnXA2 with endowments W = (0, 1)

UB (XB1, XB2) = min (XB1, XB2) with endowments W = (1, 0)

Where Xij = consumption of commodity X by consumer i = A, B of commodity j = 1, 2

Calculate the market clearing prices and the equilibrium allocation of goods (X1 and X2).