2. A consumer has preferences charaterized by the utility function u=(x1,x2)=lnx1+x2

a)What type of preferences are these? Solve for an expression for this consumer's MRS. Sketch 3 different indifference curves for this consumer.

b)Suppose M = 15, PI=1, P2= 3. Use the tangency condition MRS = p1/p2 to solve for the optimal amount of good 1. Given this, determine the optimal amount of good 2. Sketch this optimal choice on a graph of the budget set. Include an indifference curve through your optimal point.

c)Now increase income to M=21. Derive the new optimal choice and show it on a graph as in b)

d)Explain any difference between the points chosen in b) and c)