Question

1. (15 pts) Suppose Amy enjoys apple juice (A) and grape juice (G) according to U(A,G) = 3A+4G. (a) (4 pts) If apple juice costs 3 cents per ounce and grape juice costs 5 cents per ounce, and Amy has 30 cents to spend on these products, how much apple juice and grape juice should she buy to maximize her utility? (b) (3 pts) Draw the graph of her indifference map and her budget constraint, and show that the utility maximizing point occurs only on the A-axis where no grape juice is bought. Put apple juice (A) on the horizontal axis and grape juice (G) on the vertical axis. To draw the indifference map, please sketch the indifference curves for U=24, and U=30. (c) (2 pts) Assume she has income 30 cents, how would her consumption bundle change if the price of apple juice increased to 6 cents per ounce? (d) (4 pts) In part c, when the price of apple juice changes, the consumption bundle changes. Decompose the total effect of the price change on the demand for apple juice into the substitution effect and the income effect in a new graph. Label the substation effect and income effect. (e) (2 pts) Some people claim that when people are faced with two goods that are perfect substitutes, they will always buy the cheaper one. Do you agree with this claim? What if Amy's utility function changed to U(A,G) = 3A+6G?

Answer 1

1 suppose Any enjoys apple grape juices (a) according to juius (A) and U(Aja) = 3 A7 4G (a) now, apple juice costs 3 eats pnonce - or P Å = 3 cents / owate ounce and grape juice costs 5 cents pu ounce or Pa = 5 cents lounce . Any has 30 cents to spend le M= 30 Huce budget constraint will be: 1 M=APAT apa 2) 305 3A + 5G ou Now Marginal ability or apple Juius MUAS 2014: 3 A and marginal ability of crape Juius ... Mua 2 JU(A) - 4 Now, mutta 333 = 1 and Mua 4/2 = 0.8 Now as MUA > muu ; hence Any will purchase PA / P only Apple Juice and optimal amount of Canned with CamScanner

apple juice will be found by substituting Gro in the budget constraint. Hunce 30=3A + [sxo] =) A = 10 Huce, utility manimising consmption bundle will be (Asc) = (10,0) (6) Now the budget constraint ist 30 = 3 Atsu Now, the horizontal in Ancept of the budget line ů (put a ro ] 30= 3A +(580) . = 34 =) A=10 untical intucept of the budget line is [put A=0] 30= (3x0) +56 = 62.6 - Now .by Joining horizontal and uutical infucept, we can the budget constraint PQ QR. - Now the atlity manimising indifference.cnue will be targent to QR at budle. ( Asa) = (10,0) ... Now, for U=24, indistance. cave equation is . . . 24 = 34+44 39+44 . (24-49) - A =) (24-4G When Ao a=0 =) A = 24 = 8 .: whin. A=0 LO =) . 24-40 : > 11:0 =) 24-40=0 - a=6 Scanned with CamScanner

When U= 30, 303 3 A 70 44. When when a zo =) 3 A=0 =) 44= 30 =) a=715 9=0 =) 34 = 30 =) = 10 to con graph the situation .. Now we get t can graph the situat 10 + T 163 Ilr (u (10,0 To 8 Scanned with. . CamScanner

☺ Assuming m= 30 and PA increases to 6 cents pu ounce in PA= 6 cents /ounce. Whereas Put 5 ents/ounce. Now Mum - 3 = ois MU -0.8 PA MUG. P4 PA " Pu As, mon, MUA Now consuen will buy only Grape Juice and optimal consmpton bulle will be fand by substituting A=0 in the new budg it . constraint 30 = 6A + 54 . 2 30 =(680) tsa =) G=6 Now w+4 шолi мi sa bd% ощ + (А, 4) - (o, 6) d Now when budget constant is : - 30= 6 Atsu. horizontal intncept of the budget line [put a=0] :=). 30= 6A + (5 xo) 2) Ass ad uutical in Ancept of the budget line put [A=0] 30 - (680) 754 . a) a=6 Now by Joining horizontal and initial inducept, we get the new budget line QT. Which is tagut to in dit sunce conve I et at opfinal bundle (0,67 cs Scàlag Wise Can's canner

. ICI y Substitution effect . (10,0) R A tue we will get only the subs bit uton effect 10 because as the price of Apple increases, Gon Any substitutes Apple with grape Juius and consumption of apple becomes Zuo. Hunce there . is only pure substitution effect as eonsmption of apple Juice falls from 10 to o. Hace in this care, in come effect is zno. And Total eftet is equal to the substitution effect only Scanned with CamScanner