Micro-consumer theoryy

[SoniaKapoor]

Ollie has 40 dollars, which he decides to spend on x and y. Commodity x costs $13 per unit
and commodity y costs $11 per unit. He has the utility function U(x; y) = 6x2 + 4y2 and he can
purchase fractional units of x and y.
a) Ollie will choose only x.
b) Ollie will choose only y.
c) Ollie will chose some of each commodity, but more y than x.
d) Ollie will choose some of each commodity, but more x than y.
e) Ollie will choose equal amounts of the two commodities.

[bhavya jain]

b) will consume only y

[Dreyfus]

Will consume both......but more of y than good x.....

[SoniaKapoor]

Please can you tell me how did you get only Y???

[CHANGEZ]

Ollie can consume whole of one good when utility fn is of pure substitution nature i.e. U(x,y)= x+y.

Since this is not the case, for sure option 1 and 2 are wrong. to my mind option d (consume both but more of x) should be correct because the utility curve is of elliptical nature, bulge is on x-axis representing x commodity. thats what i thought..
some easy thinking logical answer would be appreciated!

[SoniaKapoor]

The ans is only y.
bhavya can u expain????

[bhavya jain]

Sonia, i perceived this problem this way. i don't know however this is correct or not.
This is a concave function, i think. Since Concave fns have boundary solutions & px>py, so the optimal consumption will lie on the vertical axis, with zero units of consumption of x & only consumption of y.

[CHANGEZ]

@bhavya, you're absolutely correct that this is a concave function and boundary sol'n will be answer. I did some calculations, Have a look:

Given that U(x,y)=6x2 + 4y2 ; income(m)=$40; P)x=$13 and P)y=$11

Budget equation: 13x + 11y=40

Case 1: Ollie consume all of x ; y=0 and x=40/13 {given that consumption can be in fraction}; U=6.(40/13).(40/13) + 0 = 59.62
Case 2: Ollie consume all of y; x=0 and y=40/11; U=0 + 4.(40/11)(40/11) = 52.89

If we compare, we see that utility is maximum when ollie consumes all of x! Lekin sonia mentioned answer "only y" hai!

[SoniaKapoor]

@bhavya thankuuu

@chulbul ....ur approach is correct but the ans is only y

[Akshay Jain]

the Marginal Utility/rupee from X is 12x/13 and from Y is 8y/11.....clearly the consumer shud consume all X and no Y as MUx/Px>MUy/Py....how the ans is Y...i dnt get dat

[Amit Goyal]

ICs are concave and utility is increasing in both x and y implying there will be a corner optimum. He has two options:
Consuming only x: utility = 6*(40/13)^2 = 56.8
Consuming only y: utility = 4*(40/11)^2 = 52.9

Answer is (a) Ollie will choose only x.

[CHANGEZ]

Thank you so much sir.. finally problem comes to its conclusion.

[SoniaKapoor]

I suppose then the answer given must be wrong.
Even i was getting confused.Thankuu sir for helping out.