Question

Maria consumes only two goods: pens and notebooks. Currently, pens cost $1 each and notebooks cost $3 each. Maria’s income is $15. The tables below show the total utility Maria receives from consuming various quantities of each of the goods. calculate the optimal consumption bundle for Maria. (Note: for full credit you must provide the correct quantities of pens and notebooks AND fill in as much of Table 3 as was necessary to arrive at your answer.)

#of Notebooks Total Utility # of Pens Total Utility

0    0 0 0

1    75 1 40

2    135 2 60

3      185 3 75   

4 230     4 87

5 . 270 5 97

6 300 6 105

7 320 7 111

Answer 1

Cost of pen = $1

Cost of notebook = $3

Income = $15

Following table shows the marginal utility per dollar of pen and the marginal utility per notebook per dollar schedule -

Notebooks	Total utility	Marginal utility	MUN/PN	Pens	Total utility	Marginal utility	MUP/PP
0	0	-	-	0	0	0	-
1	75	75	25	1	40	40	40
2	135	60	20	2	60	20	20
3	185	50	16.67	3	75	15	15
4	230	45	15	4	87	12	12
5	270	40	13.33	5	97	10	10
6	300	30	10	6	105	8	8
7	320	20	6.67	7	111	6	6

The optimal consumption bundle is the bundle corresponding to which following condition is fulfilled -

MUN/PN = MUP/PP

The above condition is fulfilled in the following cases -

Case 1 - When 2 notebooks and 2 pens are consumed

Cost of bundle = [2 * $3] + [2 * $1] = $6 + $2 = $8

Case 2 - When 4 notebooks and 3 pens are consumed

Cost of bundle = [4 * $3] + [3 * $1] = $12 + $3 = $15

Case 3 - When 6 notebooks and 5 pens are consumed

Cost of bundle = [6 * $3] + [5 * $1] = $18 + $5 = $23

It can be seen that in case of 1st bundle, total income is not utilized while third bundle is out of budget.

Only in case of IInd bundle that entire budget is utilized and optimal condition is fulfilled.

Thus,

The optimal consumption bundle for Maria is 4 notebooks and 3 pens.