In: Economics
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).
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 |