problem code : 100609MICRO

[vishruti]

A consumer has the following utility function:
U (x1, x2) = (x1 + 2)^1/2 x2^1/2

find the optimal consumption of x1 and x2 given prices p1 = 6, p2 = 1 and income
I = 10

(sorce MIT)

[nidhi]

x1=5/6,x2=17

[vishruti]

this problem has a corner solution

x1* = 0 and x2* = 10

[shashi]

income has to be greater than 12,for this problem solution to exist....if income is 100 then,x1=22/3 and x2=56...since x1 can be consume in integer form,if this the case ,then x1=21               /3   ....p1x1=6*7=42 ....since p2=1....therefor x2=58

[vishruti]

even though income = 10

we get x1 = -1/6

but we cannot consume a negative quantity of x1 , therefore we get a corner solution , all income is spent on x2 and 0 units of x1 is consumed at given prices and income

you ans also use optimization to find the answer

[shashi]

in this case x2 also turns out to be negative.....since x2=6(x1+2)...both quantity cannot be negative...there are certain norms that has to be there while answering economics related question......X-Y space must be positive and 0-0 cannot be solution...i have done enough work on consumer theory...whereever u get this quetion there might be some sort of printing mistake....i have also discuss this with my friend they also approve the argument given by me...

[shashi]

since   x2=6(x1+2).......so x2 =11 ,since income is 10 so she will consume 10 units of x2
sorry...i took the solution incorrectly as  x2=2(x1+2)