Problem 1 Standard Edgeworth Box Elvis and Miriam love listening to MP3s, x1, and watching DVDs, x2. Elvis has initially 10 DVDs and 10 MP3s, (hence we = (10, 10)). Miriam has 90 MP3s only, (so w) = (90, 0)). Utility functions of Elvis and Miriam are the same and given by: U'(X1, (2) = In(x1) + 5In(x2) for i = E, M a What are the total resources in the "economy" with Elvis and Miriam? b) Plot the Edgeworth box and mark the allocation corresponding to initial en- dowments. Argue that such an allocation is (or is not) Pareto efficient. c) Find the contract curve (collection of all Pareto efficient allocations) analytically and plot it on your graph. d) Now, let Elvis and Miriam trade. Find the equilibrium consumption of both commodities for Elvis and Miriam and the equilibrium prices. c) Suggest two other prices that support the same allocation as the cquilibrium. f) Are the markets efficient in allocating resources? (argue using the criterion of Pareto efficiency) g) Find geometrically (in the Edgeworth box) the equilibrium consumption and prices of both commodities for the new utility (perfect substitutes) given by: U'(21, 202) = 21+ 502