Given the following partial information about a consumer's purchases.He consumes only two goods. In year 1, $p_1^1=p_2^1=100,x_1^1=x_2^1=100$
In year 2, $p_1^2=100,p_2^2=80,x_1^2=120$
Over what range of quantities of good 2 consumed in year 2(i.e,$x_2^2$) could we conclude that good 1 is an inferior good.
I feel confused because I'm not informed the choices after a change in wealth under the same price system, neither under $(p_1^1,p_2^1)$ nor $(p_1^2,p_2^2).$
But the solution given by my TA is : Since $x_1^1<x_1^2$, so we need $p^2x^1>p^2x^2$, that gives $0< x_2^2< 75$. I don't know where this argument comes from and whether it is true or not.
Any help are going to be appreciated.