In Consumer Choice, we frequently encounter budget lines and indifference curves. For a given budget line, the optimization point is at the point where the indifference curve is just tangent to the budget line. For example, here is a graph used to illustrate how inferior goods behave with increases in income:
Here, as the budget line shifts to $ I_3 $, we're shown that consumption of $ z $, an inferior good, decreases. My question is: what's stopping me from drawing the indifference curve elsewhere? Why can't I draw the indifference curve tangent to $ I_3 $, just right of $ z_1 $ so that $ z_3 > z_1 $?
Sure, the MRS should be equal to the ratio of the price of the goods, but we can show that anywhere along the budget line, right?
Also, I understand that we can't draw the IC in a way that they intersect. So, I can't draw the IC for $ I_3 $ towards the end of $ I_3 $ (near the x-axis) because it'll intersect other indifference curves -- but how do we know where to draw the IC?
In other words, I can only reproduce this diagram for inferior goods because I've seen it. If I had to graphically represent this without having seen it earlier, there is no way I'd have figured that $ z_3 $ is lesser than $ z_1 $.