A consumer has the following utility function: U(x, y) =x(y+1), where x and y are quantities of two consumption goods whose prices are

P_xand P_y respectively. The consumer also has a budget of B. Therefore, the consumer's Lagrangian is

x(y+1)+(BP_xxP_yy) x

(a) From the first-order conditions find expressions for the demand functions. What kind of good is y? In particular, what happens when P_y> B?

(b) Verify that this is a maximum by checking the second-order conditions