Suppose there are two consumers, Robinson Crusoe and Friday. Both Robinson and Friday have planted coconuts and are waiting to harvest them. If it rains, then the harvest will be bad as coconuts require a lot of sunlight. But, if it is sunny, then the harvest will be very good.

Robinson lives on the rocky side of the island and his endowment is :

(gR , bR) = (6,bR) .

Friday, on the other hand, lives on the beautiful tropical side of the island and his endowment is: (gF , bF) = (8, 4) .

The probability that it is sunny on the Island is equal to 1/2 .

Both Robinson's and Friday's state sub utility functions are given by: log (c)

1. Find the equilibrium of the economy (prices and quantities) if both Friday and Robinson live in autarky. Provide prices and quantities.
2. If Robinson and Friday agree to trade, what is the equilibrium of the competitive economy? Explain your answer carefully. Provide prices and quantities.
3. Who trades what with whom? In no more than 10 lines, explain what drives trade between Robinson and Friday. That is, explain why both find trade mutually beneficial. Provide a CLEAR Edgeworth box that explains the intuition you are providing.
4. Set up and solve the planner's problem for this economy, for an arbitrary set of weights F and R.
5. Decentralize the planner's problem if F = R and bR = 10.
6. In no more that 15 lines, explain clearly how markets allow Robinson and Friday to share risk. Are they able to share all the risk in the economy?