problem code : 150609MICRO

[vishruti]

Quantities of the economy's only two goods denoted by x and y ; no production is possible . A's & B's preferences are described by the utility functions.

uA(x,y) = x + y

uB(x,y) = xy

A owns (0,5) and B owns the bundle (30,5)

determine the walrasian equilibrium price(s) and allocation(s)

[namrata]

p =1 but then in that case x2b is coming to be 17.5 which is not possible.x1 b= 17.5 x1a=12.5

[vishruti]

this answer is not correct

[vishruti]

px = 1/2 and py = 1

now you can calculate competitive equilibrium quantities for both agents

[vishruti]

i ll explain the problem in detail
 ua = x+ y so the denamd functin for xa = ma/px for px<py
                                                      = o for px> py
                                                      = [0 , ma / px] for px=py

ub = xy so the demand is xb = mb/2px , yb = mb / 2py

ma = 5py , mb = 30 px + 5 py

assume py=1 as numeraire

then ma = 5 mb=30 px + 5

substitute above in the demand functions

initially x = 30 and y = 10

lets assume px > py then

30px + 5/2px + 0 = 30 and px = 1/6 but this is contradictory so we reject this case

now if px = py

then ma = 5 mb = 35 and xb = y b = 17.5 , there is excess demand for y , markets do not clear , we reject this case as well

now if px< py then

30px + 5 / 2px + 5 / px = 30 and px = 1/2

and the markets will clear at these set of prices

therefore , at equilibrium px=1/2 py = 1 xa = 10 ya=0 xb=20 yb=10