Question

Consumer A regards the two goods as perfect complements, always wanting 2 units of good 1 for every unit of good s, where as B regards 4 units of good s and 3 units of good 2 as perfect substitutes. Initially, A has 60 units of good 1 and 75 units of good 2, and B has 140 units of good 1 and 25 units of good 2. a) Draw an Edgeworth box (put good 1 on the horizontal axis) and show the initial position of the two consumers. Explain why the initial allocation is NOT an equilibrium allocation. b) Suppose that the price of good 1 is equal to the price of good 2. On the diagram you drew in a) show the optimal bundles of the two consumers. Are the good markets clear? If not, show clearly the size of surplus of shortage in each market. c) What must be the competitive equilibrium price ratio of this economy? Explain your answer. d) Assuming that all the gains from trade were captured by A, what would be the equilibrium allocation of the two goods between A and B.

Answer 1

Q1)

UA= Min(X1, 2X2)

UB = 3X1 + 4X2

box dimensions : 200×100

Total X1= 60+140= 200

X2= 75+25= 100

initial allocation is not Competitive allocation, bcoz The two IC intersect each other

2) P1= P2,

Then Budget constraint of A,

MA = 60P1 + 75P2 = 135

So BC1: 135= X1 + X2

Now,

3)

At competitive eqm allocation

P1/P2 = MRS_B =( MU1/MU2)B = 3/4

so if P2= 1, P1 = .75

eqm price ratio = .75

4) eqm Competitive Allocation

MA = 60*.75 + 75= 120

MB = 140*.75 + 25= 130

For A