Question

1The table gives the total utility Jamal derives from the consumption of cup cakes and cream puffs. Jamal has $12 to spend on these two confectionery goods. The price of a cup cakes is $3 and the price of a cream puff is $1.50. a) Jamal's budget is $12. In order for Jamal to maximize his utility, how many cup cakes and cream puffs should he buy? b) Suppose the price of a cup cakes increase to $6. Jamal's income does not change and neither does the price of a cream puff. What combination of cup cakes and cream puffs will Jamal buy now?

      Cup cakes             Cream puffs

Quantity	TU	Quantity	TU
0	0	0	0
1	126	1	54.0
2	243	2	103.5
3	342	3	145.5
4	414	4	177.0
5	441	5	196.5

Answer 1

a) Ans:  In order for Jamal to maximize his utility, 3 cup cakes and 2 cream puffs should he buy.

Explanation:

MU = Change in TU / Change in Q

Utility maximization condition is where ;

Entire given money outlay must be spent on both the goods.
MU_cakes / P_cakes = MU_{cream puffs} /P_{cream puffs}

Budget constraint;

Y = P_cakes * Q_cakes + P_{cream puffs} * Q_{cream puffs}

$12 = ($3 * 3 ) + ( $1.5 * 2 )

Quantity	TUcakes	MUcakes	MUcakes /Pcakes	Quantity	TUcream puffs	MUcream puffs	MUcream puffs / Pcream puffs
0	0	--	--	0	0	--	--
1	126	126	42	1	54.0	54.0	36
2	243	117	39	2	103.5	49.5	33
3	342	99	33	3	145.5	42.0	28
4	414	72	24	4	177.0	31.5	21
5	441	27	9	5	196.5	19.5	13

b) Ans: Now, Jamal will buy the Combination of 1 cup cakes and 4 cream puffs.

Explanation:

MU = Change in TU / Change in Q

Utility maximization condition is where ;

Entire given money outlay must be spent on both the goods.
MU_cakes / P_cakes = MU_{cream puffs} /P_{cream puffs}

Budget constraint;

Y = P_cakes * Q_cakes + P_{cream puffs} * Q_{cream puffs}

$12 = ($6 * 1 ) + ( $1.5 * 4 )

Quantity	TUcakes	MUcakes	MUcakes /Pcakes	Quantity	TUcream puffs	MUcream puffs	MUcream puffs / Pcream puffs
0	0	--	--	0	0	--	--
1	126	126	21	1	54.0	54.0	36
2	243	117	19.5	2	103.5	49.5	33
3	342	99	16.5	3	145.5	42.0	28
4	414	72	12	4	177.0	31.5	21
5	441	27	4.5	5	196.5	19.5	13