isi 2004

[anon_econ]

A consumer consumes only two goods x and y. The price of good x
in the local market is p and that in a distant market is q, where
p > q . However, to go to the distant market, the consumer has to
incur a fixed cost C. Suppose that the price of good y is unity in
both markets. The consumer’s income is I and I > C . Let x0 be
the equilibrium consumption of good x. If the consumer has
smooth downward sloping and convex indiference curves, then
(A) (p − q) x0 = C always holds;
(B) (p − q) x0 = C never holds;
(C) (p − q) x0= C may or may not hold depending on the
consumer’s preferences;
(D) none of the above.

the way i thought about it was that he faces 2 budget constraints from which he can choose:
qx+y=M-C and px+y=M
if (x0,y0) is affordable with both, then (p-q)x0=C, but if it's not affordable with both BCs, then it's not =C. when i plotted the BCs i deduced that he would never choose a bundle that is affordable under both situations so am getting (b).
Please help!!

[lovekesh]

Vasudha
You are right. I draw both BC and their point of intersection satisfy the said condition. But if preferences are strictly convex, then both these lines can't have tangent to the indifference curve at the point of intersection. But if they are complement to each other, then they can both pass through that point. But i don't think that is going to be the case.

[lovekesh]

Oh My Bad!!!
They have already mentioned indifference curve is smooth downward sloping. B is correct.

[ritu]

hi vasudha....when u plot bc....how did u decide that whether intercept of size M/P Is greater or intercept M-C/q is greater???

[anon_econ]

Ritu, we don't know that for sure. But u can see that in 1 case the 2 BCs don't intersect and 1 lies entirely inside the other. In this case b is true for sure. The other case has 2 be examined, which is what i did.

[L]

I think answer should be (c).
We have two BCs, px+y=I and qx+y=I-C, then, it is entirely possible that at the point of intersection, one of the BCs may or  may not be tangent to indifference curve.
Somebody please confirm.