Lesson test: Preferences and utility

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Preferences and utility

1.[2p]
Why can two indifference curves never cross?

The crossing point would force two bundles on different curves to be indifferent, contradicting monotonicity

Correct

Utility functions are continuous, and continuous functions cannot cross

The answer is: The crossing point would force two bundles on different curves to be indifferent, contradicting monotonicity

Preferences are complete, so every bundle lies on exactly one curve by assumption

The answer is: The crossing point would force two bundles on different curves to be indifferent, contradicting monotonicity

Convexity bows the curves towards the origin, which keeps them apart

The answer is: The crossing point would force two bundles on different curves to be indifferent, contradicting monotonicity

2.[3p]
A consumer has $u (x, y) = x^{0.25} y^{0.75}$ and holds the bundle $(10, 60)$ . What is the marginal rate of substitution of $y$ for $x$ ?

CorrectNot quite: 2

3.[1p]
If $u$ represents a preference ranking, then so does $u^{3}$ .

True

Correct

False

The answer is: True

4.[2p]
Which quantity is unchanged when a utility function is replaced by an increasing transformation of itself?

The marginal rate of substitution

Correct

The marginal utility of $x$

The answer is: The marginal rate of substitution

The difference in utility between two bundles

The answer is: The marginal rate of substitution

The ratio of the utility numbers of two bundles

The answer is: The marginal rate of substitution

5.[2p]
With $u (x, y) = \sqrt{x} + \sqrt{y}$ , what is the utility of the bundle $(34, 34)$ , to two decimal places?

CorrectNot quite: 11.66

6.[3p]
Which of these are consequences of assuming transitivity?

Select all that apply

A best element exists to be found, so maximisation is meaningful

Correct

A consumer cannot be walked around a cycle of trades and returned worse off

Correct

Indifference curves cannot cross

Correct

Indifference curves must bow towards the origin

The answer is: A best element exists to be found, so maximisation is meaningful, A consumer cannot be walked around a cycle of trades and returned worse off, Indifference curves cannot cross

7.[3p]
Lexicographic preferences are complete, transitive and monotonic. What is true of them?

No utility function at all can represent them, which is why continuity is assumed

Correct

They are represented by a continuous utility function like any other well behaved ranking

The answer is: No utility function at all can represent them, which is why continuity is assumed

They violate transitivity once three goods are involved

The answer is: No utility function at all can represent them, which is why continuity is assumed

They are represented by a utility function, but not a differentiable one

The answer is: No utility function at all can represent them, which is why continuity is assumed

8.[3p]
Match each utility function to the preferences it describes.

$u = 2 x + 3 y$
$u = \min (x, 2 y)$
$u = \ln x + y$
$u = x^{0.4} y^{0.6}$

perfect complements
quasilinear
smoothly convex
perfect substitutes

Show the answer

$u = 2 x + 3 y$ : perfect substitutes $u = \min (x, 2 y)$ : perfect complements $u = \ln x + y$ : quasilinear $u = x^{0.4} y^{0.6}$ : smoothly convex

9.[2p]
For $u (x, y) = x^{0.4} y^{0.6}$ , what is the marginal rate of substitution at the bundle $(40, 30)$ ?

CorrectNot quite: 0.5

1.[2p] Why can two indifference curves never cross?

2.[3p] A consumer has u(x,y)=x0.25y0.75 and holds the bundle (10,60). What is the marginal rate of substitution of y for x?

3.[1p] If u represents a preference ranking, then so does u3.

4.[2p] Which quantity is unchanged when a utility function is replaced by an increasing transformation of itself?

5.[2p] With u(x,y)=x+y, what is the utility of the bundle (34,34), to two decimal places?

6.[3p] Which of these are consequences of assuming transitivity?

7.[3p] Lexicographic preferences are complete, transitive and monotonic. What is true of them?

8.[3p] Match each utility function to the preferences it describes.

9.[2p] For u(x,y)=x0.4y0.6, what is the marginal rate of substitution at the bundle (40,30)?

1.[2p]
Why can two indifference curves never cross?

2.[3p]
A consumer has $u (x, y) = x^{0.25} y^{0.75}$ and holds the bundle $(10, 60)$ . What is the marginal rate of substitution of $y$ for $x$ ?

3.[1p]
If $u$ represents a preference ranking, then so does $u^{3}$ .

4.[2p]
Which quantity is unchanged when a utility function is replaced by an increasing transformation of itself?

5.[2p]
With $u (x, y) = \sqrt{x} + \sqrt{y}$ , what is the utility of the bundle $(34, 34)$ , to two decimal places?

6.[3p]
Which of these are consequences of assuming transitivity?

7.[3p]
Lexicographic preferences are complete, transitive and monotonic. What is true of them?

8.[3p]
Match each utility function to the preferences it describes.

9.[2p]
For $u (x, y) = x^{0.4} y^{0.6}$ , what is the marginal rate of substitution at the bundle $(40, 30)$ ?