1. Consider the problem of maximizing u(c, t) subject to Pc + wl =wT + Y, where c is consumption leisure time T is the total time endowment, and Y is non wage income. Prove that if leisure is en inferior good then the labour supply function is upward-sloping.
2 Consider the problem of maximizing u a (x1, x2)3 subject to p1x1 + p2x2 = y. Derive the Marshallian demand functions and the indirect utility function, and confirm that Roy's identity holds.