Consider an exchange economy in which Marge & Homer Simpson are stranded on an island. Both get utility u(P,W) = 0 ln P+In W from P potatoes and W bottles of water, where is a parameter that reflects the island soil's ability for growing existing potatoes into additional new potatoes. Marge is endowed with 5 potatoes and 5 waters, while Homer is endowed with 10 potatoes and 0 waters. (a) Find the set of Pareto optimal allocations in state 0. Describe them in terms of Marge's bundle (PM, WM), with Homer then getting whatever is left of the island resources. (b) Find Marge's demand (best affordable quantity) for water, assuming that she knows . (c) Repeat part (b) for Homer. (d) Looking at the water market, find the equilibrium price ratio in state 0, assuming that both Marge and Homer know 0.