High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Microeconomics Textbook > Theory of Consumer Choice

Optimal Bundle (Utility Maximization)

Budget ConstraintPrevious Section
Changes in IncomeNext Section
Popular Courses
Find My Course
0:00 / 0:00

Optimal Bundle (MUx/Px = MUy/Py)


The optimal bundle is also called utility maximization and it is the point where the marginal utility per dollar (which is the marginal utility divided by the price) of each good is the same.
 MUxPx=MUyPy\boxed{\text\ \frac{MUx}{Px}= \frac{MUy}{Py}}


Example: If the price of good X is $10 and its marginal utility is 100 while the price of Y is $20, then the marginal utility of Y must be
200
at utility maximization. If the marginal utility of Y was 300 then you should consume more units of good
Y
and less units of good
X
.

If we take the formula from above and rearrange it we would get the formula below which tells us the exact same thing.

 MUxMUy=PxPy\boxed{\text\ \frac{MUx}{MUy}= \frac{Px}{Py}}

0:00 / 0:00

Example: Optimal Bundle (MUx/Px = MUy/Py)

The price of apples is $1.50 and the price of peaches are $2.50. Mark gets a marginal utility of 30 from his last apple and a marginal utility of 40 from his last peach consumed. Based on this information, how should he change his consumption of the two fruits?

A) consume more peaches
B) consume more apples
C) do not change consumption as he is at his optimal consumption bundle
D) cannot be determined

B.

MUa/Pa = 30/1.5 = 20
MUp/Pp = 40/2.5 = 16
Since 20 > 16 he should always get more of the bigger number so consume more apples. It's giving him more happiness per dollar.
0:00 / 0:00

Optimal Bundle (Indifference Curve and Budget Constraint)

The optimal bundle is also called the utility maximization point or the consumer equilibrium. This is a combination of two goods that provides you a given utility at the lowest possible budget. You can also think of it as a combination that gives you the maximum utility given your budget.

  • In the diagram above points A and B give the
    same
    level of utility (because they are on the same indifference curve).
  • However, point B is on a
    higher
    budget.
  • This means point A is the best point to be at so it is the optimal bundle.
  • At point A the indifference curve is tangent to the budget line which means their slopes are the same. The slope of the indifference curve is called the MRS (Marginal Rate of Substitution) and the slope of the budget line is -Px/Py.
 MRS= −PxPy\boxed{\text\ MRS =\ \frac{-Px}{Py}}


MUxPx=MUyPy\boxed{\frac{MUx}{Px}=\frac{MUy}{Py}}



MUxMUy=PxPy\boxed{\frac{MUx}{MUy}=\frac{Px}{Py}}


0:00 / 0:00

Example: Optimal Bundle (Indifference Curve and Budget Constraint)

Brenda is currently consuming 5 milkshakes and 3 sandwiches a week. The price of each milkshake is $4 and sandwiches are $10. If milkshakes are plotted on the X axis and sandwiches on the Y axis, what would be her MRS (Marginal Rate of Substitution) at utility maximization?

A) -2.5 B) -0.4 C) -0.6 D) -3.3
B At utility maximization the MRS = -Px/Py = -4/10 = -0.4

Extra Practice
Practice: Optimal Consumption 2
The table shows Jerry's utility from consuming fried chicken and burgers. Suppose Jeffrey has $12 to spend and the unit price of fried chicken and burgers are $1 and $2, respectively. What is Jerry's optional consumption bundle?
Practice: Optimal Consumption 1
Derek’s marginal utility for consuming coffee is 4. His marginal utility for eating a slice of pizza is 10. Each cup of coffee cost $2 and each slice costs $4.50. Which of the following is true?
a) Derek at his optimal consumption bundle
b) Derek will consume more coffee and less pizza
Suppose Paulina is consuming her optimal consumption bundle of goods 1 and 2. Which of the following must be true?
WhenMUxPx>MUyPy\frac{MU_x}{P_x}>\frac{MU_y}{P_y}
Which of the following is true about a consumer with the given budget line and two indifference curves
In the diagram above, suppose the consumer's income is $25,200, price of X is $1575 and price of Y is $700.
a) What is the optimal quantities of X and Y?
X =
8
The price of apples is $1.50 and the price of peaches are $2.50. Mark gets a marginal utility of 30 from his last apple and a marginal utility of 40 from his last peach consumed. Based on this information, how should he change his consumption of the two fruits?
Jessica consumes chocolate bars and chips. Chocolates cost $2 per unit and chips cost $4 per unit. How many units of each good will she consume if she has $8 to spend?
Optimal is 0 chocolates and 2 chips
Arnold can consume either oranges or kiwi. The price of an orange is $1 and the price of a kiwi is $1. At Arnold's current consumption bundle, his marginal utility from oranges is 10 and his marginal utility from kiwi is 7.5. Arnold is better off
Practice: Optimal Consumption
The condition of optimal consumption, for any pair of products, X and Y, is
Practice: Marginal Utility 2
Derek’s marginal utility for consuming coffee is 4. His marginal utility for eating a slice of pizza is 10. Each cup of coffee cost $2 and each slice costs $4.50. Which of the following is true?
A consumer's optimal bundle happens to be a point on the x-axis. Which of the following are true?
In general, a consumer chooses the consumption bundle that
Practice: Utility
Economists usually assume that consumers: