This exercise walks you through the main steps to decompose a price change into a substitution and income effect.

Suzanne's utility function is given byU(x, y) =1log(x) +1log(y), wherelog(u)denotes natural logarithm.22

Letthepricesbegivenbypx=py=2andherincomeism=200.

1. Find the Marshallian demandsxm(px,py,m)andym(px,py,m). What's the optimal utility level at this bundle? [If you prefer, you do not need to show all work. However, showing your work will get partial credit if you make a mistake.] [4 points]
2. Call the above Marshallian demands bundleA= (xm,ym). Draw the budget constraint, bundleA, and the indifference curve that goes through the bundle. [You do not need to be very precise with the indifference curve. Only remember the shape of the indifference curves for a Cobb-Douglas utility function.] [4 points]
3. Now assume that the price ofxfalls topx= 1. Find the new Marshalian demand functions and call this bundleB= (x, y). Draw the new budget constraint, bundleB, and the indifference curve that
4. goes through it.Do it on the same graph as in part (2).[6 points]
5. Find bundleC= (xs, ys), where the movement from bundleAto bundleCcan be interpreted as the substitution effect (SE). Recall that bundleClies on the same indifference curve as bundleA. [Hint: You need to use expenditure minimization!] [8 points]
6. From part (4), what's the minimum expenditure needed to buy bundleC? Then, what is the in- come compensation needed to keep this agent as 'happy' as she was before the price fall? [Hint: a compensation can be either positive or negative.] [4 points]
7. If theSEis the movement from bundleAtoC, then the income effect,IE, is the movement from bundleCto bundleB. Isxnormal or inferior? Isynormal or inferior? Justify your answers. [4 points]