Alice and Bart are the only two persons on a desert island. There are only two goods Bananas(B) and Nachos(N).

Alice utility function: U(Na, Ba) = N*B

Bart utility function: U(Nb, Bb) = 2N + B

Alice is endowed with 3 units of bananas and 8 units of nachos. Bart is endowed with 6 units of bananas and 8 units of nachos.

Let the price of nachos equal one. In competitive equilibrium, what will be the price for bananas? How many bananas and nachos will Alice and Bart consume in equilibrium? What are Alice's and Bart utility?