Problem 1 Elvis and Miriam both love listening to MP3s (2,) and watching DVDs (x2). Initially, Elvis has 10 DVDs and 10 MP3s (hence w = = (10, 10)). Miriam has just 90 MP3s (sow = (90,0)). Utility functions for Elvis and Miriam are the same and given by U(m, 1) = In(2) + 5(x) i= E,M (a) What are the total resources in the "economy" with Elvis and Miriam. Use this to determine the dimensions of the Edgeworth Box. (b) Find analytically the contract curve (collection of all Pareto efficient allocations and plot it on your graph. Now let Elvis and Miriam trade. Find the equilibrium consump- tion of both commodities for Elvis and Miriam and the equilibrium (relative) prices. (d) Are the markets efficient at allocating resources? Use the criterion of Pareto efficiency. (e) (extra credit challenge) Find geometrically (using the Edgeworth box model) the equilibrium consumption and prices of commodities for the perfect substitute utility: U'(1], 22) = 21 + 5r2