Georgina consumes only pasta (good x)and wine(goody). Her utility function is given by U(x,y)=3lnx+lny.

(a)Consider only bundles with both x>0andy>0. Are Georgina's preferences monotone?Are they strictly monotone? Does this utility function satisfy diminishing MRS?

(b)Find the expenditure-minimising bundle(x,y)as a function of the prices px and py,and the target utility U.

(c)(c.1)Find the expenditure necessary to attain the utility U as a function of the prices px and py,and the target utility U itself. If the prices are px=1,py=1,obtain the expenditure necessary to attain the utility U=ln16.

(c.2)What is Georgina's utility-manimizing bundle if her income is M=16and prices are p x=3 and py=1?What utility does she attain?

(d)The owner of the store where Georgina buys her groceries has a special offer: any customer that buys more than 2 units of pasta is charged only p'x=1 per unit for any quantity in excess of 2 units (but for the first two units of x customers still have to pay p x=3 perunit). Recall that Georgina's income is M=16andpy=1

(d.1)What is (are) the equation(s) describing Georgina's budget line under this special offer?

(d.2)What is Georgina's optimal consumption with this special offer?