Question

An exchange economy consists of two individuals---consumer A and consumer B with preferences over two goods---goods X and Y. Suppose consumer A is initially endowed with 9 units of good X and 6 units of good Y and consumer B is initially endowed with 91 units of good X and 14 units of good Y. Both consumer A and consumer B have identical preferences with the following marginal rates of substitution: MUX - 1 YA MRS, = MUX - and MRS, = = 1 Yg MU 2 x MU, 2 X At the resulting competitive equilibrium, what is the price of good Y (with the price of good X normalized to 1)? a) 10. b) 20. c) 2. d) 1. e) 5 Hint: You will need to first find an expression for the demand of each consumer for each of the goods.

Answer 1

option A) 10

MA = 9+6py of A Q) CA (X,Y)= (9,6), B = (91, 14), 80x=100, Ý=20, MRSA = YA MRS B = YB QXA QXB. Let Px=1, then at ce, Y A tyB = ý = 20 for A, at Eqm YA = P (at Eqm MRS = Px1P4) 9XA Py YAPY = QXA from B. C x Px typy = MA MA endowment Income 80. xtypy = MA - yPy + gly = MA M B= a1 + 14 ly. 3 UR = MA, YzqmA 80. YA+yß = 20 OMA AMB = ý = do. 3py 3py 2 (9+6 ly + 91+ 414) = 6oly 100+ 20 Py = 3oly - 100=10 py Py*= 10 option A) Ang