Question 3 (20 marks).Mary's utility function is

U(x, y) =x^1/2+1/2y

(a) Obtain the MRS. Draw the indifffference curves forU= 1andU= 2. Make sure to identify

the intersections with each of the axes. (5 marks)

(b) Supposepy= 1and Mary's income isM= 3. In a new graph, show the income effffect and

substitution effffect (on the demand ofx) of a drop in the price ofxfrompx= 2topx= 1.

(5 marks)

(c)(c.1) What is the income elasticity ofxfor Mary's utility function? (1 mark)

(c.2) Is there any pair of pricespxandpyand incomeM >0for which Mary's utility

maximising bundle hasy= 0? If your answer is "yes," then provide an example of such

prices and income. If your answer is "no," then explain why this is the case. (2 marks)

(c.3) Is there any pair of pricespxandpyand incomeM >0for which Mary's utility

maximising bundle hasx= 0? If your answer is "yes," then provide an example of such

prices and income. If your answer is "no," then explain why this is the case. (2 marks)

(d) There is a new store around the corner wherepx= 1andpy= 3. However, they have a

special offffer: for any amount ofYthat Mary buys, she gets the same amount ofXfor free.

Mary's income isM= 3. Draw Mary's budget line. Write down the equation of this line.

Find Mary's utility-maximising bundle. (5 marks)