Coursenotes_ECON301

This consumer has a utility function that allows us

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Unformatted text preview: 6 + 4 (PX) 1 PX XA* = 9 YA = PX2 PY2 YA = 12 12 YA* = 1 XB = X XA* XB* = 1 YB = Y YA* YB* = 9 This example illustrates that the individual with a linear indifference curve (consumer B) will dictate the price ratio, while the individual with the quasilinear indifference curve will dictate the final demands in the pure exchange economy. 120 PURE EXCHANGE EXAMPLE (1 LIONTIEF & 1 LINEAR CONSUMER) Consider a simple pure exchange economy with two consumers, A and B, and two goods, X and Y. UA = min {2X , Y} A = (XA , YA) = (2,3) UB = X + 3Y B = (XB , YB) = (3,2) We can figure out consumer A's marginal rate of substitution as: MRSA = ? Now let's turn our attention to Consumer B. This consumer has a utility function that allows us to determine their marginal rate of substitution and an endowment that constrains their utility as follows: UB = X + 3Y B = (XB , YB) = (3,2) We can figure out consumer B's marginal rate of substitution as: MRSB = MUXB MUYB = __1__ 3 At the consumer equilibrium, the price ratio is dictated by consumer B and is simply: MRSB = _1_ = PX 3 PY This gives us the relationship between PX & PY as: 3PX = PY Back to Consumer A... At the consumer equilibrium, the equations consumer A needs to satisfy are: 2XA = YA (1) (1a) (1b) 121 PX XA + PY YA = MA Subbing (1) into (2) we get: PX XA + 2 PY XA = MA PX XA + 2 PY XA = 2 PX + 3 PY and we know that 3 PX = PY must hold in equilibrium, so... PX XA + 6 PX XA = 2 PX + 9 PX 7 PX XA = 11 PX XA = 11 / 7 (2) Now let's go back and find YA, remember that the equations consumer A needs to satisfy are: 2XA = YA Subbing (1) into (2) we get: PX XA + PY YA = MA PX YA + PY YA = MA PX YA + PY YA = 2 PX + 3 PY and we know that PX = 1/3 PY must hold in equilibrium, so... 1/6 PY YA + PY YA = 2/3 PY + 3 PY PY YA + 6 PY YA = 4 PY + 18 PY 7 PY YA = 22 PY YA = 22 / 7 We should notice that Consumer A's demands lie on both the equilibrium price vector (common budget line) and on the kink line defined by their perfect complement preferences. (1) (2) 122 It is now elementary to find Consumer B's...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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