Question

78) Jack has an income of $150 per month that he can spend on two goods: shoes and jeans. From the following table, estimate the bundle that maximizes Jack's well-being. Jeans ($10/pair) Marginal Benefits ($) Quantity (units) Shoes ($20/pair) Marginal Benefits (S) 0 35 40 33 33 2 22 28 15 23 4 10 20 5 7.5 15 6
Please include an explanation of the answer. Thank you.

Answer 1

Let X be the number of shoes purchases and Y be the number of jeans purchased.

The budget constraint is

20 X + 10 Y = 150

To find the bundle the maximizes Jacks well being, we first have to calculate the total cost for the quantity of shoes and Jeans purchased.

Total cost = Quantity x Price per unit

Total cost for 1 unit of shoe = 1 x $ 20 ( $ 20)

Total cost for 2 unit of shoe = 2 x $ 20 ( $ 40)

Total cost for 3 unit of shoe = 3 x $ 20 ( $ 60)

Total cost for 4 unit of shoe = 4 x $ 20 ( $ 80)

Total cost for 5 unit of shoe = 5 x $ 20 ( $ 100)

Total cost for 6 unit of shoe = 6 x $ 20 ( $ 120)

Total cost for 1 unit of Jeans = 1 x $ 10 ( $ 10)

Total cost for 2 unit of Jeans = 2 x $ 10 ( $ 20)

Total cost for 3 unit of Jeans = 3 x $ 10 ( $ 30)

Total cost for 4 unit of Jeans = 4 x $ 10 ( $ 40)

Total cost for 5 unit of Jeans = 5 x $ 10 ( $ 50)

Total cost for 6 unit of Jeans = 6 x$ 10 ( $ 60)

The table below shows the total cost for the quantity of shoes and Jeans purchased.

Quantity(Units)	Shoes ($20 per pair)	jeans($10 per pair)
	Marginal benefits	Marginal benefits	Total cost shoes	Total cost jeans
0	_	_	_	_
1	40	35	$20.00	$10.00
2	33	33	$40.00	$20.00
3	28	22	$60.00	$30.00
4	23	15	$80.00	$40.00
5	20	10	$100.00	$50.00
6	15	7.5	$120.00	$60.00

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Next we have to calculate the marginal cost for shoes and Jeans at each level of quantity.

Marginal cost is the change in the total cost when an additional unit is purchased.

Change in total cost Marginal cost Change in Quantity

$20 0 Marginal cost 1 unit of shoe 1 0

Marginal cost 1 unit of shoe = $20

$40 $20 Marginal cost 2 unit of shoe 2 1

Marginal cost 2 unit of shoe = $20

$60 $40 Marginal cost 3 unit of shoe 3 2

Marginal cost 3 unit of shoe = $20

$80 $60 Marginal cost 4 unit of shoe 4 3

Marginal cost 4 unit of shoe = $20

$100 $80 Marginal cost 5 unit of shoe 5 4

Marginal cost 5 unit of shoe = $20

$120 $100 6 5 Marginal cost 6 unit of shoe

$10 S0 Marginal cost 1unit of Jeans 1 0

Marginal cost 1 unit of Jeans = $ 10

$20 $10 Marginal cost 2 unit of Jeans 2 1

Marginal cost 2 unit of Jeans = $ 10

$30 $20 Marginal cost 3 unit of Jeans 3 2

Marginal cost 3 unit of Jeans = $ 10

$40 $30 Marginal cost 4 unit of Jeans 4 3

Marginal cost 4 unit of Jeans = $ 10

$50 $40 Marginal cost 5 unit of Jeans 5 4

Marginal cost 5 unit of Jeans = $ 10

$60 $50 Marginal cost 6 unit of Jeans 6 5

Marginal cost 6 unit of Jeans = $ 10

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The table below shows the total cost and marginal cost for shoes and jeans

Quantity(Units)	Shoes ($20 per pair)	jeans($10 per pair)
	Marginal benefits	Marginal benefits	Total cost shoes	Total cost jeans	Marginal cost shoes	Marginal cost jeans
0	_	_	_	_	_	_
1	40	35	$20.00	$10.00	$20.00	$10.00
2	33	33	$40.00	$20.00	$20.00	$10.00
3	28	22	$60.00	$30.00	$20.00	$10.00
4	23	15	$80.00	$40.00	$20.00	$10.00
5	20	10	$100.00	$50.00	$20.00	$10.00
6	15	7.5	$120.00	$60.00	$20.00	$10.00

From the above table, we observe that at 5 units of shoes and 5 units of jeans, the marginal benefit of purchasing shoes and jeans equals the marginal cost.

Consumers choose to consume the bundle of goods whose marginal benefits equals marginal benefits. Hence Jacks bundle that maximizes well being is the quantity of shoes and Jeans whose marginal benefits equals marginal cost.

The bundle that maximizes Jack's well being = ( 5 Shoes , 5 Jeans)

This bundle also satisfies Jack's budget constraint.

5 shoes costs $ 100 and 5 Jeans costs $ 50. The total cost is $ 150 which is also Jack's income per month