Question

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) = 5A/B/. 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

Please show all steps so I can fully understand how to solve. Thank you

Answer 1

A) Utility can be maximized by equating the MRS and the Price Ratio.

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. 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 that the consumer has to be compensated for the price increase at the new price level.

5Aч 84 Quus uCA,B)= M РoA+ PoB Audger onstaînt -3/4 в4 MAS muA MuB A PA Roctio PA PB B Рaica Rati MRS 3PAA Y PAA M PA At 3PAA A ЧРА 8- 3 PA M ЧРа x 1в ЧРе Total Pica ect suhsutution tte et ь)м name Ebect. en MSA MufA

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.

er A vauabon Compensating J

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. AC or DB is the equivalent Variation.

e i er A variatien auivalent