Two Consumers Jim and Pam Both Have Opera Tickets and Movie

Essay

Two consumers Jim and Pam both have opera tickets and movie tickets.They wish to exchange tickets with each other.Given their utility functions $$U ^ { I } \left( O _ { J } , M _ { J } \right)$$ and $$U ^ { P } \left( O _ { P } , M _ { P } \right)$$ ,show that their marginal rates of substitution need to be equal for any given distribution of tickets to be efficient.