General Equilibrium Consider a market with two goods, x and z, and two consumers
ID: 1163282 • Letter: G
Question
General Equilibrium
Consider a market with two goods, x and z, and two consumers, A and B. The utility functions for consumers A and B are as follows
2. General Equilibrium Consider a market with two goods, z and z, and two consumers, A and B. The utility functions for consumers A and B are as follows UB and the initial endowments for each consumer are eA= (4,2) eB= (2,6) where consumer B is endowed with 2 unit of good x and 6 units of good z, respectively. a) Draw the Edgeworth Box (Don't worry about the shape of the utility curves. Just pick a general shape that we have used before). b) Derive the contract curve.Explanation / Answer
a) Here the edgeworth box will have dimensions (6, 8) i.e. total x in the economy is 6 and total z in the economy is 8
Hence the edgeworth box will look like:
b) Contract curve is set of all points which are pareto effecient or points such that no one can be made better off without making the other worse off. Therefore to derive it we must find locus of all points such that marginal rate of substituion of both the consumer is equal.
MRS for consumer 1 : MUxa/MUza
= 1/2(Za/Xa)
Similarly MRS for consumer 2 will be: MUxb/MUzb =
= 2(Zb/Xb)
Equating these two we get
1/2(Za/Xa) = 2(Zb/Xb)
or (Za/Xa) = 4(Zb/Xb)
or (Za/Xa) = 4(8 - Za /6- Xa)
Cross- multiplying and simplifying we get Za = 32/6 Xa
Therefore the contract curve is Za = 32/6 Xa for Xa belongs to (0, 6).
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