Question 2 (20 marks).Jack consumes only bread (goodx) and cheese (goody). His utility

function is given by

U(x, y) = 4 lnx+ lny.

(a) Consider only bundles with bothx >0andy >0. Are Jack's preferences monotone? Are

they strictly monotone? Does this utility function satisfy diminishing MRS? (5 marks)

(b) Find the expenditure-minimising bundle(x, y)as a function of the pricespxandpy, and the

target utilityU. (5 marks)

(c)(c.1) Find the expenditure necessary to attain the utilityUas a function of the pricespx

andpy, and the target utilityUitself. If the prices arepx= 1,py= 1, obtain the

expenditure necessary to attain the utilityU= ln 32. (3 marks)

(c.2) What is Jack's utility-maximising bundle if his income isM= 5and prices are

px= 1andpy= 1? In a well labelled graph, represent Jack's budget line and his

utility-maximising consumption bundle. (2 marks)

(d) Jack's sister, Elena has a utility function given by

V(x, y) = max{2x, y},

where the functionmax{x, y}gives the maximum ofxandy(for instance,max{1,2}= 2,

max{6,3}= 6,max{5,5}= 5, etc.)

(d.1) Provide the utility-maximising consumption bundle as a function of the pricespx,py,

and Elena's income, denoted byI. (2 marks)

(d.2) Provide the expenditure-minimising consumption bundle as a function of the pricespx,

py, and the target utilityV. (2 marks)

(d.3) Suppose thatpx< py. What is the income elasticity ofx? (1 mark)