Coursenotes_ECON301

# Consider a simple pure exchange economy with two

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Unformatted text preview: n that allows us to determine their marginal rate of substitution and an endowment income that constrains their utility as follows: 111 UA = UA(XA,YA) = X0.4Y0.6 MA = PX XA + PY YA = 7 PX + 3 PY We can figure out consumer A's marginal rate of substitution as: MRSA = MUXA MUYA = 0.4 X-0.6Y0.6 0.6 X0.4Y-0.4 = 2YA 3XA At the consumer equilibrium, the two equations consumer A needs to satisfy are: MRSA = 2YA = PX 3XA PY Rearranging (1) we get: PX XA + PY YA = MA 3XA PX = 2YA PY (1) (2) (3) Meaning we can get demands for XA and YA by subbing (3) into (2) as follows: PX XA + (3/2) PX XA = MA (5/2) PX XA = MA XA = 2MA 5 PX (4) and we know that MA = 7 PX + 3 PY is the endowment income of consumer A, so we sub this in for the MA in (4) to get: XA = 14 PX + 6 PY 5 PX XA = 14/5 + _6PY__ 5 PX (5) (2/3) PY YA + PY YA = MA 112 (5/3) PY YA = MA YA = 3MA (6) 5 PY and we know that MA = 7 PX + 3 PY is the endowment income of consumer A, so we sub this in for the MA in (6) to get: YA = 21 PX + 9 PY 5 PY YA = 9/5 + _21PX__ 5PY (7) 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 income that constrains their utility as follows: UB = UB(XB,YB) = X0.65Y0.35 MB = PX XB + PY YB = 5 PX + 9 PY We can figure out consumer B's marginal rate of substitution as: MRSB = MUXB MUYB = 0.65 X-0.35Y0.35 0.35 X0.65Y-0.65 = 13YB 7XB At the consumer equilibrium, the two equations consumer B needs to satisfy are: MRSB = 13YB = PX 7XB PY Rearranging (1B) we get: PX XB + PY YB = MB 7 XB PX = 13 YB PY (1B) (2B) (3B) Meaning we can get demands for XB and YB by subbing (3B) into (2B) as follows: PX XB + (7/13) PX XB = MB 113 (20/13) PX XB = MB XB = 13MB 20 PX (4B) and we know that MB = 5 PX + 9 PY is the endowment income of consumer B, so we sub this in for the MB in (4B) to get: XB = 65 PX + 117 PY 20PX XB = 13/4 + _117PY__ 20 PX (5B) (13/7) PY YB + PY YB = MB (20/7) PY YB = MB YB = 7MB 20 PY (6B) an...
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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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