GE ques

[Shweta Singhal]

Q1: There are two consumers A & B following utility functions and endowments as :
           uA(xA , yA) = a ln xA+ (1-a) ln yA    , wA= (0,1)

            uB(xB , yB) = min(xB, yB)    , wB= (1,0)

    Calculate the market clearing prices and equilibrium allocation.


Q2:  Person A has the utility function of  uA(xA , yA)= xA+yA & Person B has the utility function  uB(xB , yB)= max(xB,yB).
A & B have endowments of (1/2 , 1/2). What is the equilibrium relationship between P1 and P2. & What is the equilibrium allocation?

Q3: Agent A and B both consume the same good in pure exchange economy. Agent A is originally endowed with wA(15,12) and agent B with wB(97,4). They have same utility function u(x,y)= x power 1/3 , y power 2/3.
Let Px = 1 then Py is?

[Kiran]

ans to problem no 2
P1/P2 = 1
equilibrium allocation = [(1,0)(0,1)] Or [(0,1)(1,0)]

[Kiran]

ans to problem1
px/py = 1
Equilibrium is (1/2,1/2)(1/2,1/2)
and i think there can be one one soln..

[Kiran]

i will reply tmrrw

[Shweta Singhal]

Hey Kiran thanks fr d solutions.. Bt Can u plz explain d full solutions..
Actually i dont knw hw to solve dese kind of ques..

[kiran]

try to draw edgeworth box
locate endowment
draw IC of both individual
find out demand function
look at three cases
p1=0 , p2>0
p1>0, p2 =0
P1=1, p2= p
find out income of each individual in each case and then find out demand again and check market clearing conditions (dd of each good by two individual should be equal to endowment)and u will get the solutions
one more thing when p=0  then dd is(0,infinity)
one more sol is p1>0, p2 =0 ((0,0)(1,1))

[duck]

Hello shweta.. :)

Q1> if a =1/2 , px=py
      if a>1/2 , px/py= 2
      if a<1/2, px/py=1/2

Q2> as Kiran said.

Q3> the price ratio , px/py= 1/14

(hint: find the demand for both the individuals and
just see at what price ratio, demand by both of them = total endownment)


:)

[kiran]

i dont think that value of a will affect CE. as the function is cobb Douglas. no matter what is your value of a it will be a quasi concave function. so i case of positive prices we need to find out only slope of line passing through endowment intersecting 45 degree line and tangential to IC of consumer one....
also we need to check for p1 or p2 =0

[duck]

Hello kiran,

tht slope also depends upon the value of "a"
In this  case, the slpoe is  ay/ (1-a)x


so the equilibrium price ratio will actually depend upon the value of a..
and hence, the market clearing price ratio, px/py= a/1-a

[kiran]

 hey can you negate this sol p1>0, p2 =0 ((0,0)(1,1))

[duck]

hello kiean.. :)

this is also a solution of this que..

:)