a) Check for “regularity conditions” to see if the standard tangency method is applicable: test whether preferences are differentiable, insatiable, and strictly convex.
(b) If you found in (a) that all three conditions are met, find the optimal affordable bundle.
(c) If you found in (a) that at least condition fails, clearly state which one and (roughly) sketch some indifference curves to demonstrate what the issue is. Note that for any given problem, you will do either (b) or (c), never both. For this problem set, do not try to find the optimal bundle when the standard method does not apply.
1.u(x, y, z) = 3 ln(x) + 2 ln(y 2 ) + 12z, px = 10, py = 5, pz = 2, m = 100.
2. u(x, y) = 8x − 3x^ 2 + 15y − 2y ^2 − 7000, px = 6, py = 20, m = 5.