Consider the following problems, write down the individual demand functions for X and Y for both consumer A and B, then write down the market clearing conditions and find the competitive equilibrium price and the C.E. allocation if there's any exist. If there is no CE exist, write down the reason. (Let Px = p, Py =1 and XA represents the demand function for good X of consumer A, YA represents the demand function for good Y of consumer A, use the same way to indicate the demand functions for consumer B. Also, determine if the allocation ( (1,1), (2,2) ) is feasible and individually rational for both problems.

a) U_a(X^a, Y^a) = X^a Y^a, U_b(X^b, Y^b) = (X^b+1)Y^b, the initial allocation is ( (2,0), (0,1) ).

b) U_a(X^a, Y^a) = min { X^a, Y^a }, U_b(X^b, Y^b) = min { X^b, 2Y^b }, the initial allocation is ( (5, 0), (0,10) )