Please answer and explain

1. Consider an exchange economy with two consumers, A and B, and two commodities, x and y. Consumer A is endowed with 2 units of x and 4 units of y, while B is endowed with 2 units of x and 2 units of y. Their preferences are given by u(x4, yA) = xAy (for which MRSA = and uB (xB, yB) = (xB)2(yB) (for which MRSB _ 2yb) xB ), respectively. a. Determine if the initial allocation is Pareto efficient. b. Determine if the allocation ((1,4),(3,2)) is individually rational. c. Determine if the allocation ((3,2),(1,4)) is envy-free. d. Assuming the agents were able to trade at prices px and py, write B's budget equation/constraint. e. A's and B's demand functions for x and y are given respectively by: x4 (Px, Py) = Px+2Py ya (Px, Py) = Px +2py Px Py x B (P x, Py) = 4(Px + Py ) 2(Px + Py) , yB (P x, Py) = 3px 3Py Explain how to determine the equilibrium prices; that is, set up the market clearing conditions for x and y. You do not have to solve the equations