Question

During zoom class lecture fill in the information and answer the questions below:
units MUa MUper $ TU MUb MUper$ TU Price of A=$1; Price of B= $2;budget=$10
1 10 24
2 8 20
3 7 18
4 6 16
5 5 12
6 4 6
How many units of A and B should you buy?
What is your maximum TU from your budget of $10?
If your budget goes up to $14, how many units of A and B should you buy? TU for that?

Answer 1

Units	MUa	MUa per $	TUa	MUb	MUb per $	TUb
1	10	10	10	24	12	24
2	8	8	18	20	10	44
3	7	7	25	18	9	62
4	6	6	31	16	8	78
5	5	5	36	12	6	90
6	4	4	40	6	3	96

MUa per $ = MUa / Price of A

TUa = Sum of MUa

MUb per $ = MUb / Price of B

TUb = Sum of MUb

At optimal point; (MUa per $ = MUb per $)

The above condition is satisfied for the three combination of goods:

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Combination 1: Unit of Good A = 1; Units of Good B = 2

(MUa per $ = MUb per $) = 10

Cost of buying this bundle: 1*$1 + 2* $2 = $5

Budget to spend is $10.

Cost of buying this bundle is less than the budget to spend. It means consumer is not fully utilizing budget.

Hence, this bundle does not maximize utility subject to budget constraint.

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Combination 2: Unit of Good A = 2; Units of Good B = 2

(MUa per $ = MUb per $) = 8

Cost of buying this bundle: 2*$1 +4* $2 = $10

Budget to spend is $10.

Cost of buying this bundle is equal to the budget to spend. It means consumer is fully utilizing budget.

Hence, this bundle does maximize utility subject to budget constraint.

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Combination 3: Unit of Good A = 4; Units of Good B = 5

(MUa per $ = MUb per $) = 6

Cost of buying this bundle: 4*$1 + 5* $2 = $14

Budget to spend is $10.

Cost of buying this bundle is more than the budget to spend. It means consumer can't afford this bundle.

Hence, this bundle does not maximize utility subject to budget constraint.

Answer: Consumer would buy 2 units of good A and 4 units of good B

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2 units of good A gives TU of 18

4 units of good B gives TU of 78

=> TU from utility maximization bundle = 18 + 78

=> TU from utility maximization bundle = 96

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Now budget goes from $10 to $14.

Combination 1: Unit of Good A = 1; Units of Good B = 2

(MUa per $ = MUb per $) = 10

Cost of buying this bundle: 1*$1 + 2* $2 = $5

Budget to spend is $14.

Cost of buying this bundle is less than the budget to spend. It means consumer is not fully utilizing budget.

Hence, this bundle does not maximize utility subject to budget constraint.

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Combination 2: Unit of Good A = 2; Units of Good B = 2

(MUa per $ = MUb per $) = 8

Cost of buying this bundle: 2*$1 +4* $2 = $10

Budget to spend is $14.

Cost of buying this bundle is less than the budget to spend. It means consumer is not fully utilizing budget.

Hence, this bundle does not maximize utility subject to budget constraint.

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Combination 3: Unit of Good A = 4; Units of Good B = 5

(MUa per $ = MUb per $) = 6

Cost of buying this bundle: 4*$1 + 5* $2 = $14

Budget to spend is $14.

Cost of buying this bundle is equal to the budget to spend. It means consumer is fully utilizing budget.

Hence, this bundle does maximize utility subject to budget constraint.

Answer: Consumer would buy 4 units of good A and 5 units of good B

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4 units of good A gives TU of 31

5 units of good B gives TU of 90

=> TU from utility maximization bundle = 31 + 90

=> TU from utility maximization bundle = 121