Lesson 4

Question 1

What is the utility function for Perfect Substitutes?

Answer 1

U(x1,x2)=ax1+bx2U(x1​,x2​)=ax1​+bx2​

Question 2

What is the shape of the indifference curves for Perfect Substitutes?

Answer 2

Downward sloping straight lines.

Question 3

What is the utility function for Perfect Complements?

Answer 3

U(x1,x2)=min⁡(ax1,bx2)U(x1​,x2​)=min(ax1​,bx2​)

Question 4

What is the shape of the indifference curves for Perfect Complements?

Answer 4

L-shaped lines (or “intersecting lines” forming right angles).

Question 5

What is the general form of a Quasi-linear utility function?

Answer 5

U(x1,x2)=f(x1)+x2U(x1​,x2​)=f(x1​)+x2​

Question 6

What is the key visual characteristic of Quasi-linear indifference curves?

Answer 6

They are vertical shifts of each other (they have the same slope).

Question 7

What is the general form of a Cobb-Douglas utility function?

Answer 7

U(x1,x2)=x1cx2dU(x1​,x2​)=x1c​x2d​

Question 8

How are Cobb-Douglas indifference curves described?

Answer 8

Well-behaved and strictly convex.

Question 9

What is a Marginal Utility?

Answer 9

The additional utility gained from consuming one more unit of a good.

Question 10

What is the formula for the Marginal Rate of Substitution (MRS) using marginal utilities?

Answer 10

MRS=−MUx1MUx2MRS=−MUx2​MUx1​​

Question 11

What is the MRS for a Cobb-Douglas function U(x1,x2)=x1cx2dU(x1​,x2​)=x1c​x2d​?

Answer 11

MRS=−cx2dx1MRS=−dx1​cx2​​

Question 12

What is Ordinal Utility?

Answer 12

Only the ranking of utility matters; the magnitude of the difference between values is not meaningful.

Question 13

What is Cardinal Utility?

Answer 13

The magnitude and difference between utility values are meaningful.

Question 14

What is the purpose of a Monotonic Transformation of a utility function?

Answer 14

To create a new function that represents the same underlying preferences.

Question 15

What is the key property that is preserved under a monotonic transformation?

Answer 15

The MRS (the slope of the indifference curve) remains the same.

Question 16

What is the fundamental requirement for any utility function?

Answer 16

It must preserve the original preference relations of the consumer.

Question 17

If two bundles have the same utility value, what does this imply?

Answer 17

The consumer is indifferent between the two bundles.

Question 18

What is the relationship between utility functions and indifference curves?

Answer 18

An indifference curve connects all bundles that yield the same utility level.