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Unformatted text preview: ply in terms of endowments of the goods. XA + XB = 5/7 + 2/7 XA + XB = 1 XA + XB = X YA + YB = 5/11 + 6/11 YA + YB = 1 YA + YB = Y So, in both the market for X and the market for Y, demands are equal to supplies and we have market clearing (equilibrium). 171 Now, let's look at this in an Edgeworth Box diagram...
B Core ICA IC B Here we have our original situation...Person A has their endowment of (1/4, 3/4) and Person B has their endowment of (3/4, 1/4). Both consumers have an indifference curve through the endowment point. This means that along these indifference curves each consumer is just as happy without trade.
X=1 OA Now let's consider how we get from this original situation to our final Pareto optimal competitive equilibrium... Y=1 ICA 2/7 O B Slope = -7/11 5/11 6/11 Now we can see that from the original endowment these consumers (guided by their preferences, i.e. indifference curves) trade goods X and Y such that the prevailing price ratio, PX / PY, is 7/11 and the tangency line separates both indifference curves at the point of tangency (i.e. where PX / PY = MRSA = MRSB). This point of tangency turns out to be where A A B B (X , Y , X , Y ) = (5/7, 5/11, 2/7, 6/11). ICB OA 5/7 X=1 172 Alright, now let's see if the contract curve is bowed in the right direction... We know that consumer A and consumer B have utility functions that are both Cobb-Douglas form as follows: UA = XA1/2YA1/2 MRSA = __1/2YA__ 1/2 XA UB = XB1/4YB3/4 MRSB = __1/4YB__ 3/4 XB And we know that the Pareto Optimal allocations must satisfy MRSA = MRSB, so... __1/2YA__ = __1/4YB__ 1/2 XA 3/4 XB and we want our contract curve coordinates in terms of consumer A so we can convert consumer B's demands into: YB = Y YA So... XB = X XA _1/2__ YA__ = __1/4 1/2 XA 3/4 YA__ = __1/8 XA 3/8 Y YA __ X XA Y YA __ X XA YA (X XA) = 1/3 (Y YA ) XA YA X YA XA + 1/3 YA XA = 1/3 Y YA [X 2/3 XA] = 1/3 Y YA = _____1/3 Y________ X (2/3) XA Now the "bow" is either the second derivative of this mess above or we can compare on the main diagonal to estimate the 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.
- Spring '10