Question

) The table below gives the utility from pens and pencils.
Quantity of pens Total utility from pens Quantity of pencils Total utility from pencils
0 0 0 0
1 90 1 70
2 155 2 120
3 200 3 150
4 225 4 165
5 240 5 174
6 246 6 176
(i) If the consumer has an income of $4, pens cost $1, and pencils cost $.20, which of the combinations maximizes the consumer's utility?
(ii) If the consumer has an income of $4, pens cost $1, and pencils cost $.20, what is the consumer's total utility when he or she maximizes utility?

Answer 1

i)

$$I=4$$

$$p_{pen}=1, p_{pencil}=0.2$$

$$\frac {MU_{pen}}{p_{pen}}=\frac {MU_{pencil}}{p_{pencil}}$$

$$MU_{pencil}=0.2 MU_{pen}$$

3 pens and 5 pencils will be bought.

ii)

$$TU=TU_{pens}+TU_{pencils}$$

$$TU=200+174=374$$