I 5. Imagine a threeperson economy in which the rst commodity is gardening services, the consumption of which makes one's yard more beautiful, and the second good is food. Imagine that two of the consumers in this society live in adjacent houses, while the third lives on the other side of a particularly large mountain. Consumption by the third consumer of gardening services generates no extemality for the other consumers, but each of the others generates a positive externaiity for her neighbor thIOugh the consumption of gardening services. To be precise, imagine that consumers 1 and 2 have utility functions of the fonn Vim) = tutti) + 1M3?) + :6; where w : [0,oo) > R is a strictly increasing, strictly concave, and dif- ferentiable function. Note weil that consumers 1 and 2 get just as much utility out of their neighbor's yard as they do out of their own, and their utility for food is linear. (You were warned that this is a very special setting.) Also imagine that consumer 3 has a utility function of the form V303) = wins?) + 1:3. There is a social endowment of gardening services and food. (a) Suppose the social endowment is initially allocated evenly among the three consumers. What will be the corresponding Walrasian equilibrium (with externalities)? (b) Characterize the set of Pareto efcient allocations of the social endow- ment. Is the equilibrium allocation in (a) Pareto efficient