Question

There are two goods in the world, ice (x) and tea (y), and two consumers, Anna and Elsa. Elsa's utility function is uF(xE, YE) = QE (y) and her endowment is we = (4, 4). Anna's utility function is uA (24, 74) = x4.74 and her endowment is wa = (0,0).

Answer 1

Given: T^E = -4, T^A = 4, P_X = 1, u^E(X^E,Y^E) = X^E.(Y^E)³ , u^A(X^A,Y^A) = X^A.Y^A

NOW, Budget Constraint: P_X.X + P_Y.Y = P_Xw_X + P_Yw_Y + T     [where, T = (Transfers) – (Taxes)]

b) Elsa’s budget constraint: 1. X^E + P_Y.Y^E = 1(4) + P_Y (4) – 4,

                                    or, X^E + P_Y.Y^E = 4P_Y

Equilibrium occurs at: MRS^E = P_X/ P_Y

Thus, for Elsa: (Y^E)³/ X^E.3(Y^E)² = 1/ P_Y or, Y^E = 3X^E/P_Y

Setting in Elsa’s B.L., we get: 4X^E = 4P_Y or, X^{E ­}= P_Y andY^E = 3

c) Anna’s budget constraint: 1. X^A + P_Y.Y^A = 1(0) + P_Y (0) + 4

                                       or. X^A + P_Y.Y^A = 4

Equilibrium for Anna: Y^A/ X^A = 1/ P_Y or, Y^A = X^A/ P_Y

Setting in Anna’s B.L., we get: 2X^A = 4 or, X^A = 2 and Y^A = 2/ P_Y