I. Consider a two-person, two-good exchange economy in which the utility functio

Question

I. Consider a two-person, two-good exchange economy in which the utility

functions are

Ui  (x1i,x2i) = x1i * x2i for i=1; 2 and the initial endowments are

w1 = (1,3) for agent 1, and

w2 = (3,1) for agent 2.

a. Find the individual demand Di(p) for i=1,2 and the market excess demand

E(p)?

b. Show that any price vector p = (p1; p2) where p1 = p2 along with the

allocation (x1; x2) where x1 = x2 = (2; 2) is an equilibrium?

c. Keep everything the same except change the utility function to min{xi1,x2i},

find the new individual demand, and excess demand?

Explanation / Answer

a) using two points (1,3) and (3,1) the eq of line concept

Q = - P + 4

b) since (2,2) satisfy the above,the vector of line from origion and (2,2) satisy the above eq,i.e put (2,2) in above demand curve both the side becomes 2 .Therefore eq is satisfied so it is in equilibrium

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