person A is endowed with a car that he values at $200, and with $1,000 in cash. person B has no car, values A's car at $350, and is endowed with $1,000 in cash. how do i formally describe the utility functions for this problem. Agent i has utility over car and money equal to: ui = Xi + mi where mi denotes the amount of money consumed by agent i. XA equals zero if agent A does not consume the car, and 200 if he does. XB equals zero if agent B does not consume the car, and 350 if he does.

First question is What are the competitive equilibrium prices?

Second question is At any competitive equilibrium allocation, who gets the car?