1. Suppose Alice has a utility function over cookies and marshmallows given by: UA(CA, MA) = (CA)3/4 (MA) 1/4 and suppose Bob has a utility function given by: UB(CB, MB) = (CB) Z (MB) 1/2 Their aggregate endowments of cars and motorcycles are wc = 30 and WM = 15. a) Find Alice and Bob's marginal utilities for both goods (MUA, MUA, MU and MUR). Use these to find Alice and Bob's marginal rates of substitution for cookies and marshmallows (MRSCM and MRSCM) b) Derive an equation for the contract curve that expresses MA as a function of CA.) Draw the contract curve you found in b) on an Edgeworth Box for this economy. Use the horizontal axis to represent allocations of cookies and the vertical axis to represent allocations of marshmallows. Have Alice's origin be in the bottom left corner of the box and Ben's origin in the top right corner. Indicate where the contract curve intercepts the sides, floor, and/or ceiling of the Edgeworth Box. Indicate what the slope of the contract curve 1s as well. d) Suppose Alice and Bob's individual endowments of cookies and marshmallows are (wa, wh) = (16,5) and (w, WM) = (14, 10). Can Alice and Ben gain by trading? Assess this in 2 ways: 1) Do their individual endowments satisfy the equation MRSy = MRS . 2) Does Alice's initial endowment satisfy the equation for the contract curve? e) Suppose a Walrasian Auctioneer calls out prices for cookies and marshmallows denoted by Pc and PM. Find the equilibrium prices (PE, PM) and equilibrium allocations (C*A, M*A), (C*B, M*B). Let the marshmallows be the numeraire good