Question 2: There are two goods and two consumers with identical consumption sets X= R++2 and utility functions: uA(xA1,xA2)=xA13(xA2)3uB(xB1,xB2)=3(xB1)3+xB2 and endowments A=(2,243241) and B=(243241,2). 1. State the consumer problems. 2. Find the demand functions - solely prices (p1,p2)R++2 such that xi1,xi2>0 for i{A,B} have to be considered. 3. Find xA1/(p2/p1). Illustrate xA1/(p2/p1). (Hint: Let r=p2/p1 and replace p2/p1 with r in xA1 and find xA1/r.) 4. Show there are Walrasian equilibria with prices (p1,p2)=(1/2,1),(p1,p2)=(1,1) and (p1,p2)=(2,1). 5. Discuss the possible economic implications of multiplicity of Walrasian equilibria. 6. Find the set of Pareto optimal allocations. Illustrate in an Edgeworth box. Question 2: There are two goods and two consumers with identical consumption sets X= R++2 and utility functions: uA(xA1,xA2)=xA13(xA2)3uB(xB1,xB2)=3(xB1)3+xB2 and endowments A=(2,243241) and B=(243241,2). 1. State the consumer problems. 2. Find the demand functions - solely prices (p1,p2)R++2 such that xi1,xi2>0 for i{A,B} have to be considered. 3. Find xA1/(p2/p1). Illustrate xA1/(p2/p1). (Hint: Let r=p2/p1 and replace p2/p1 with r in xA1 and find xA1/r.) 4. Show there are Walrasian equilibria with prices (p1,p2)=(1/2,1),(p1,p2)=(1,1) and (p1,p2)=(2,1). 5. Discuss the possible economic implications of multiplicity of Walrasian equilibria. 6. Find the set of Pareto optimal allocations. Illustrate in an Edgeworth box