The question I am given is the following: Consider an economy that has only three goods, mineral water, orange juice, and wine available in ﬁxed amounts, and three agents, A, B and C. So in this economy agents have no money initially. There are perfectly competitive markets for these three goods. The agents are not allowed to hold any negative amount of goods. Answer the following questions.
(a) Suppose that A owns all the mineral water, B owns all the orange juice, and C owns all the wine. A only likes orange juice, B only likes wine, and C only likes mineral water. What are the equilibrium prices for mineral water, orange juice and wine and the equilibrium quantities consumed by each individual?
(b) Now suppose that A owns everything and A only likes drinking orange juice, both B and C own nothing, both B and C like drinking wine only. Discuss the equilibrium quantities consumed by each individual.
(c) Now suppose that A equally likes these three goods, B equally likes the mineral water and orange juice, but does not like wine at all, and C only likes wine. Without considering who owns mineral water, orange juice, or wine initially, what allocations are Pareto optimal?
My question is about sub-questions (b) and (c). For (b), if A owns everything and B and C own nothing, apparently there will be no trade. So what is the point for asking this question? For (c), if there is no utility function, how could I tell what is Pareto optimal? I really wish someone could teach me how to answer this kind of question and show me some examples. Thank you, and I wish you a happy new year.