Question

Question 2 (Choice) Mrs. Gordon has 3 sons. She spends $100 on each boy during the holiday season to buy them chocolate and gummy bears. Assume the price of chocolate (good 1) is $2 and the price of gummy bears (good 2) is $5 per pound. Being a clever economist, she has estimated that the utility functions of the three boys are uFred(x1, 2) xjaz, wTed(xi, x2) = /x122 and uEd(x1,x2) =x12 a. For each boy find his marginal utility of chocolate and his marginal utility of gummy bears (MUi) b. Find each boy's marginal rate of substitution (MRS) between the two goods. For (that is as you go down each boy, how does the MRS change along an indifference curve an indifference curve increasing xi and decreasing T2)? c. How much chocolate and candy will Mrs. Gordon give each boy (assume she wants $100 for that boy's gift)? to maximize each boys utility subject to spending exactly т — d. If she had decided to spend $120 on each boy, how would her choice change? m e. If she had decided to spend even more, can you predict how her choice would change? Show this graphically, no need to derive the new choice.

Answer 1

Combination	Chocolate	Gummy Bear	TU fred	MU Fred	TU Ted	MU Ted	TU Ed	MU Ed
A	50	0	0	-	7.07	-	50	-
B	47.5	1	2256.25	2256.25	8.89	1.81	48.5	1.5
C	45	2	8100	5843.75	10.71	1.81	47	1.5
D	42.5	3	16256.25	8156.25	12.52	1.81	45.5	1.5
E	40	4	25600	9343.75	14.32	1.80	44	1.5
F	37.5	5	35156.25	9556.25	16.12	1.80	43.5	1.5
G	35	6	441000	8943.75	17.92	1.80	41	1.5
H	32.5	7	51756.25	7656.25	19.70	1.78	39.5	1.5
I	30	8	57600	5843.75	21.48	1.78	38	1.5
J	27.5	9	61256.25	3656.25	23.24	1.76	36.5	1.5
K	25	10	62500	1243.75	25	1.76	35	1.5
L	22.5	11	61256.25	(1243.75)	26.74	1.74	32.5	2.5
M	20	12	57600	(3656.25)	28.47	1.73	32	0.5
N	17.5	13	51756.25	(5843.75)	30.18	1.71	30.5	(1.5)
O	15	14	44100	(7656.25)	31.8	1.62	29	(1.5)
P	12.5	15	35156.25	(8943.75)	33.54	1.74	27.5	(1.5)
Q	10	16	25600	(9665.25)	35.16	1.62	26	(1.5)
R	7.5	17	16256.25	(9343.75)	36.73	1.11	24.5	(1.5)
S	5	18	8100	(8156.25)	38.23	1.5	23	(1.5)
T	2.5	19	2256.25	(5843.75)	39.58	1.35	21.5	(1.5)
U	0	20	0	(2256.25)	40	0.42	20	(1.5)

Chocolates Ulted) (Ted २५641618024 Gummy Beans

Answer a :-

Refer table

Answer b :-

MRS =

Δ2/Δzl

=1/2.5=0.4

Answer c :-

Fred will receive 25 chocolates and 10 Gummy Bears.

Ted will receive 20 Gummy Bears and zero chocolates.

Ed will receive 50 chocolates and 0 Gummy Bears

Answer d :-

If she decides to spend dollar 120 then and again she would purchase only chocolates for Ed, only Gummy Bears for Ted and and equally divide the the total budget for read there by purchasing 30 units of chocolates and 12 units of Gummy Bears

Answer e :-

If she decides to spend more she will end up purchasing only chocolates for Ed, only Gummy Bears for Ted and the midpoint that is the equal division of budget between chocolate and Gummy Bears for fred.