Free Practice Quiz Question List

2 Utility and Its Representations Online Quiz Questions

Use this free practice quiz with 20 questions to review 2 Utility and Its Representations, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A consumer’s preferences are represented by $U(x,y)=xy$ . Bundle A is $(3,2)$ , and bundle B is $(2,2)$ . Which bundle is preferred according to this utility representation?

A
Bundle A, because its utility is higher.
B
Bundle B, because its utility is higher.
C
The bundles are equally preferred because they have the same amount of $y$ .

Written response

1 point

What term describes utility that records the order of preferences rather than a measurable amount of happiness?

True or false

1 point

True or false: If a differentiable, strictly increasing transformation is applied to a utility function, the consumer’s marginal rate of substitution remains unchanged.

A
True
B
False

Choose all

1 point

For perfect substitutes represented by $U(x,y)=ax+by$ , select all statements supported by the model.

A
Its indifference curves are straight lines.
B
Its MRS is constant across bundles.
C
Its MRS necessarily falls as the consumer gets more $x$ .
D
If the goods have equal marginal utility per dollar, every affordable bundle on the budget line provides the same utility.

Written response

1 point

For $U(x,y)=x^2y$ , calculate the MRS of $x$ for $y$ at $(x,y)=(4,3)$ . Enter the numerical value, with no unit.

Choose one

1 point

A consumer has perfect-substitutes utility $U(x,y)=2x+y$ , with prices $p_x=4$ and $p_y=1$ . Based on marginal utility per dollar, which good provides more utility per dollar?

A
Good $x$ , because its marginal utility per dollar is higher.
B
Good $y$ , because its marginal utility per dollar is higher.
C
Either good, because their marginal utilities per dollar are equal.

True or false

1 point

True or false: If one bundle has utility $10$ and another has utility $5$ , the first bundle provides twice as much happiness.

A
True
B
False

Choose all

1 point

For a consumer with perfect-substitutes utility $U(x,y)=ax+by$ and prices $p_x$ and $p_y$ , select all correct statements about the budget decision.

A
The relevant comparison is between $a/p_x$ and $b/p_y$ .
B
If $a/p_x>b/p_y$ , buying $x$ gives more utility per dollar.
C
If $a/p_x>b/p_y$ , buying $y$ gives more utility per dollar.
D
If $a/p_x=b/p_y$ , every affordable bundle on the budget line provides the same utility.

Choose one

1 point

Along an indifference curve, what does the MRS of $x$ for $y$ describe?

A
The change in utility from increasing $x$ while holding $y$ constant.
B
The local amount of $y$ the consumer is willing to give up for another unit of $x$ while remaining equally preferred.
C
The amount of money spent on $x$ divided by the amount spent on $y$ .

Open ended

1 point

For positive quantities, show how taking the natural logarithm of $U(x,y)=x^{1/2}y^{1/2}$ gives an equivalent utility representation. Explain why the transformed function represents the same preferences.

Choose one

1 point

For $U(x,y)=xy$ , what is the marginal utility of $y$ at a bundle where $x=7$ ?

A
$7$
B
$1$
C
$14$

Written response

1 point

For perfect-substitutes utility $U(x,y)=x+2y$ , calculate the MRS of $x$ for $y$ . Enter the numerical value, with no unit.

True or false

1 point

True or false: In the representation $U(x,y)=x+2y$ , one unit of $y$ contributes as much utility as two units of $x$ .

A
True
B
False

Choose one

1 point

In standard consumer theory, what does a utility function’s numerical value represent?

A
A utility value directly measures the consumer’s happiness.
B
Utility values represent preference rankings, not measurable amounts of happiness.
C
The difference between two utility values measures the strength of the consumer’s preference.
D
Utility values can be compared across consumers as units of satisfaction.

Choose one

1 point

For any real-valued utility function $U$ , which transformation is guaranteed to preserve its preference ranking without requiring additional domain restrictions?

A
Replacing every utility value with twice that value.
B
Replacing every utility value with its negative.
C
Replacing every utility value with its square.
D
Replacing every utility value with its reciprocal.

Written response

1 point

If $U(x,y)=xy$ , what is the marginal utility of $x$ at the bundle $(x,y)=(2,5)$ ?

Choose one

1 point

Which description fits the standard utility representation of perfect substitutes?

A
Their indifference curves are curved, and their MRS increases as consumption changes.
B
Their indifference curves are curved, and their MRS is always zero.
C
Their indifference curves are straight lines, and their MRS is constant.
D
Their indifference curves are straight lines, and their MRS must be one.

Choose one

1 point

For $U(x,y)=x+2y$ , which statement correctly interprets the utility contributions of the two goods?

A
One unit of $y$ contributes the same utility as one unit of $x$ .
B
One unit of $y$ contributes the same utility as two units of $x$ .
C
One unit of $x$ contributes the same utility as two units of $y$ .
D
The consumer is unwilling to substitute one good for the other.

Fill in the blank

1 point

For the Cobb–Douglas utility function $U(x,y)=x^{1/2}y^{1/2}$ , calculate utility at the bundle $(x,y)=(4,9)$ . Enter the numerical utility value: .

Fill in the blank

1 point

A consumer's utility is $U(x,y)=x^{1/2}y^{1/2}$ . If $x=4$ and the target utility is $10$ , what value of $y$ achieves that utility? Enter the quantity of $y$ : .

2 Utility and Its Representations Online Quiz Questions

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