Question

In: Economics

Kathy love bagels and cream cheese. She spends her income (I) of $20 on bagels (B)...

Kathy love bagels and cream cheese. She spends her income (I) of $20 on bagels (B) and cream cheese (C) the price of a bagel (PB) is $2 and the price of cream cheese (Pc) is $4. The following table summarizees the data on her marginal utility (MU) and marginal utility per dollar (MU/P) for each bagel and cream cheese.

Bagels (Pb = $2) Cream cheese (Pc = $4)

Unit MUb MUb/PB Unit MUc MUc/Pc
1st 18 1st 20
2nd 16 2nd 16
3rd 14 3rd 12
4th 12 4th 8
5th 10 5th 4
6th 8 6th - -
7th 6 7th - -
8th 4 8th - -
9th 2 9th - -
10th 0 10th - -

a) Fill in the table.
b) Construct her budget constraint ( that is I as function of B and C) and list all offordable integer consumption bundles.
c) compere MUb / PB and MUc / Pc to find her consumer optimum

d) Calculate total utility for each affordable integer bundle, and show if total utility reaches its maximum at the consumer optimum obtained in part (c).

Solutions

Expert Solution

a) The table is completed below. Divide the marginal utility with the price to get MU/P for both goods

Unit MUB MUB/PB MUC MUC/PC
1 18 9 20 5
2 16 8 16 4
3 14 7 12 3
4 12 6 8 2
5 10 5 4 1
6 8 4 0 0
7 6 3
8 4 2
9 2 1
10 0 0

b) Budget constraint is 20 = 2B + 4C. Affordable bundles that exhaust the budget include:

Bagels Cream cheese
0 5
1 4.5
2 4
3 3.5
4 3
5 2.5
6 2
7 1.5
8 1
9 0.5
10 0

c) Consumer optimum is when Bagels purchased are 6 units and Cream cheese purchased are 2 units. MU/P is same at 3 for this bundle and the income is also exhausted (6*2 + 2*4) = 20

d) TU for (2, 4) = 34 + 56 = 90

TU for (4, 3) = 60 + 48 = 108

TU for (6, 2) = 78 + 36 = 114

TU for (8, 1) = 88 + 20 = 108

See that total utility is maximum when Bagels purchased are 6 units and Cream cheese purchased are 2 units

Unit TUB TUC
1 18 20
2 34 36
3 48 48
4 60 56
5 70 60
6 78 60
7 84 60
8 88 60
9 90 60
10 90 60

Rahul Sunny answered 2 years ago
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