Question

In: Economics

1The table gives the total utility Jamal derives from the consumption of cup cakes and cream...

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

Expert Solution

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	TU_cakes	MU_cakes	MU_cakes /P_cakes	Quantity	TU_{cream puffs}	MU_{cream puffs}	MU_{cream puffs} / P_{cream 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	TU_cakes	MU_cakes	MU_cakes /P_cakes	Quantity	TU_{cream puffs}	MU_{cream puffs}	MU_{cream puffs} / P_{cream 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

Rahul Sunny answered 2 years ago

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