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Unformatted text preview: umer B's marginal rate of substitution as: MRSA = MUXA MUYA = __5__ 2 At the consumer equilibrium, the equation consumer A needs to satisfy is: MRSA = _5_ = PX 2 PY (1B) So now that we have the equilibrium price ratio. Since only the ratio matters we can use the relationship PX = PY in consumer B's demands below (we can derive consumer A's demands from consumer B's...more in a second) 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 = 2X + 4Y1/2 B = (XB , YB) = (3,14) We can figure out consumer A's marginal rate of substitution as: MRSB = MUXB MUYB = ___2___ 2Y1/2 = YB 176 At the consumer equilibrium, the two equations consumer B needs to satisfy are: MRSB = YB 1/2 = PX PY YB = PX2 PY2 Subbing (1) into (2) we get: PX XB + PY YB = MB PX XB + PX2 = MB PY XB = MB  PX PX PY (3) (1) (2) and we know that MB = 3 PX + 14 PY is the endowment income of consumer B, so we sub this in for the MB in (4) to get: XB = 3 PX +14 PY  PX PX PY XB = 3 + _14 PY__  PX PY PX XB = 3 + _14PY__  PX PY PX = 3 + 28_ 5 / 2 5 = 3 + 56 / 10 25 / 10 XB* = 6.1 YA = PX2 PY2 YA = 52 22 YB* = 6.25 177 (4) XA = X XB* XA* = 8.9 YA = Y YB* YA* = 8.75 This example illustrates that the individual with a linear indifference curve (consumer A) will dictate the price ratio, while the individual with the nonlinear indifference curve will dictate the final demands in the pure exchange economy. Now, what about the Edgeworth Box for this problem? Recall, in the first example (2 CobbDouglas consumers) we derived the contract curve in terms of YA mostly because this gives us a familiar reference point in our usual northeast quadrant space. With quasilinear preferences, the contract curve will be the level of consumption of the quasilinear good for the individual that has the quasilinear preferences. So, in the example above consumer B is quasilinear in...
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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.
 Spring '10
 sning
 Economics

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