Question

Quantity of Tacos	Marginal Utility from Tacos	Quantity of Music Downloads	Marginal Utility from Music Downloads
1	10	1	8
2	8	2	6
3	6	3	4
4	4	4	2
5	2	5	1

1. Laura consumes both tacos and music downloads. The table above shows her marginal utility from these. What is her total utility from purchasing four music downloads?
2. Now assume Laura’s weekly income is $12, the price of taco is $2, and the price of music downloads is $1. What is the utility maximization quantity of tacos and music downloads if she spends her entire $12 on these two goods?

Answer 1

Ans. Total Utility = Cumulative sum of Marginal Utility

=> Total Utility of Tacos, TUt = 10 + 8 + 6 + 4 + 2 = $30

And total utility of Music Downloads, TUd = 8 + 6 + 4 + 2 + 1 = $21

a) Total utility from 4 music downloads, TU = 8 + 6 + 4 + 2 = $20

b) Budget constaint of Laura when she purchased T tacos and D music downloads,

2T + D = 12

Slope of budget line, Pt/Pd = price of taco/ price of music download

Slope of Indifference curve, Marginal Rate of Substitution, MRS = MUt/MUd (at each quantity)

At the level of profit maximization,

MRS = Pt/Pd

=> MRS = 2/1 and budget constraint is also satisfied.

This occurs when she consumes 4 units of tacos and 4 music downloads.

At this point total utility = $48

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