Consider commodity space where x1 is food and x2 is everything else. Allow food to have the price p1, and allow everything else to have the price of dollars, so p2 = $1. Denote income as m.
(a) Write out your budget set using mathematical set notation. (you do not need to label the currency.)
(b) Now let us assume you need a minimal amount of food, x1 to stay alive. Rewrite this budget set using mathematical set notation with this additional (and reasonable) assumption.
(c) Graph this new budget set. Be sure to label both the horizontal and vertical axes and any vertical and horizontal intercepts (this time it will be in variables not actual numbers). Lightly shade in the area that represents the budget set.
(d) Is this new budget set convex? [HINT: if you draw a line between any two points in the set (including on the boundary) does the line stay inside the set (inside here meaning it can be on the boundary but does not go outside the set).]