Question:
A) Consider the problem of maximizing u(c,l) subject to pc + wl = wT + Y, where c is consumption, l is leisure time, T is the total time endowment, and Y is non-wage income. Show that if leisure is an inferior good, then the labour supply function is upward-sloping.
B) Given the problem of maximizing ln x subject to α ≥ x2, when α > 0, confirm that the envelope theorem holds.