Question

CV=Compensating Variation EV=Equivalent Variation

3. Utility maximization under constraint, substitution and income effect, CV and EV (20 points) Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A,B) = 5A1/4B3/4. While Luke would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose PA increase. Show graphically the income, substitution effect and total effect and explain. c. Suppose PA increase. Show the graph for CV and EV and explain.

Answer 1

A) Utility can be maximized by setting up the lagrangean maximization problem.

PA A PeB - M Sulyect to Мax 2. PAA+ PeB M logangan 5A34 hleh/e APA O дА ав м -о 1

APА в бnз дм Уч я. АЗУЧ в Уч PA БX3 ч уч ч Ве Рa i*А 3 3 РaA PoB Suritrci ng abouu in (3) PAA + 3 РАA ЧРАА м м А - 4РА в- 3РАА Рe м ЧАА ЗРА В - ЗМ uРо

B) Substitution Effect is the effect of price change alone and income effect takes into account only the change in the demand due to changes in income or purchasing power only. Total Price Effect is the sum of substitution and income effect.

AB is the original Budget Line and AB' is the pivoted Budget Line after Pa increases. E1 is the original consumption bundle , E2 is the intermediate consumption bundle and E3 is the final consumption bundle. Line tangent to original consumption bundle IC1 at E3 is the intermediate budget line with the income that consumer has to be compensated for the price increase at the new price level.

The distance on the x axis between the bundle E1 and E3 is the substitution effect and between E3 and E2 is the income effect and total price effect is given by distance on x- axis between E1 and E2.

C) Compensating Variation is the amount of income the consumer has to give up or compensated for , to remain at the same utility level at the new prices. Budget line shifts from AB to AB'. Compensating Variation is given by the amount the budget line AB' has to be shifted at the new price level in order to remain at the original utility level. AC or B'D gives the Compensating Variation. E1, E2 and E3 stand as before.

Pouc Etct Total ь)м Subititution te et naome Etbect е MAM MuPA

er A vauaton lompensating

And Equivalent Variation is how much a person is willing to give up to avoid a price increase. Again, AB is the original Budget Line and AB' is the Budget line after price shift. CD Is the budget line that is drawn at original price level and at the final utility level. It is drawn at the income level that the consumer would want to remain at the final utility level but at the original prices, so as to avoid the price change. E1 is the original , E2 is the intermediate and E3 is the final consumption bundle .

AC or DB is the equivalent Variation.

ei er A quivalent variaten