Morris Zapp and Philip Swallow consume wine and books. Morris has an initial endowment of 60 books and 10 bottles of wine. Philip has an initial endowment of 20 books and 30 bottles of wine. They have no other assets and make no trades with anyone other than each other. For Morris, a book and a bottle of wine are perfect substitutes. His utility function is U(b,w) = b + w, where b is the number of books he consumes and w is the number of bottles of wine he consumes. Philip’s preferences are more subtle and convex. He has a Cobb-Douglas utility function, U(b,w) = bw. In the Edgeworth box below, Morris’s consumption is measured from the lower left, and Philip’s is measured from the upper right corner of the box.
(a) On this diagram, mark the initial endowment and label it E. Use red ink to draw Morris Zapp’s indifference curve that passes through his initial endowment. Use blue ink to draw in Philip Swallow’s indifference curve that passes through his initial endowment. (Remember that quantities for Philip are measured from the upper right corner, so his indifference curves are “Phlipped over.”)
(b) At any Pareto optimum, where both people consume some of each good, it must be that their marginal rates of substitution are equal. No matter what he consumes, Morris’s marginal rate of substitution is equal to __________ When Philip consumes the bundle, (bP, wP), his MRS is ___________ Therefore every Pareto optimal allocation where both consume positive amounts of both goods satisfies the equation __________ Use black ink on the diagram above to draw the locus of Pareto optimal allocations.
(c) At a competitive equilibrium, it will have to be that Morris consumes some books and some wine. But in order for him to do so, it must be that the ratio of the price of wine to the price of books is ______________ Therefore we know that if we make books the numeraire, then the price of wine in competitive equilibrium must be ___________
(d) At the equilibrium prices you found in the last part of the question, what is the value of Philip Swallow’s initial endowment? _____________ At these prices, Philip will choose to consume ___________ books and _________ bottles of wine. If Morris Zapp consumes all of the books and all of the wine that Philip doesn’t consume, he will consume _________ books and __________ bottles of wine.
(e) At the competitive equilibrium prices that you found above, Morris’s income is _________ Therefore at these prices, the cost to Morris of consuming all of the books and all of the wine that Philip doesn’t consume is (the same as, more than, less than) _________ his income. At these prices, can Morris afford a bundle that he likes better than the bundle (55, 15)? _____________
(f) Suppose that an economy consisted of 1,000 people just like Morris and 1,000 people just like Philip. Each of the Morris types had the same endowment and the same tastes as Morris. Each of the Philip types had the same endowment and tastes as Philip. Would the prices that you found to be equilibrium prices for Morris and Philip still be competitive equilibrium prices? ___________ If each of the Morris types and each of the Philip types behaved in the same way as Morris and Philip did above, would supply equal demand for both wine and books? _____________