02 utility

Question 1

What does marginal utility measure?

Answer 1

Marginal utility measures the additional utility gained from consuming one
more unit of a good.

Diyelim ki:

1 bardak portakal suyu içtiğinde 50 birim fayda hissediyorsun.
2 bardak içtiğinde toplam faydan 80 oldu.
O zaman ikinci bardaktan gelen ekstra fayda = 80 - 50 = 30
Bu 30, ikinci bardak için marjinal faydadır.

Question 2

How is marginal utility calculated?

Answer 2

MUi​ (x1​,x2​) = ∂u​ /∂xi​ . (x1​,x2​)

Sol taraf = x i malının marjinal faydası, yani bir birim daha tüketilirse alınacak ek fayda

Sağ taraf = Fayda fonksiyonunun xi ‘ye göre türevi, yani bu malın faydayı ne kadar artırdığı

Question 3

What does the derivative show on a graph, and how is it related to marginal utility?

Answer 3

It shows the slope of the tangent line. For marginal utility, it shows how fast utility is changing.

Question 4

What does a positive marginal utility mean?

Answer 4

It means the utility function is locally increasing — more of good i is better for the consumer.

Question 5

What does a negative marginal utility indicate?

Answer 5

It means more of the good is worse for the consumer — utility decreases.

Question 6

Does the “exact value” of marginal utility always matter?

Answer 6

No, the exact value depends on the “utility function” used. What matters is whether it’s positive or negative.

Question 7

How can two different utility functions represent the same preferences?

Answer 7

If they rank consumption bundles in the same order, they represent the same preferences—even if their marginal utility values differ.

Question 8

What is The Marginal Rate of Substitution (MRS)?

Answer 8

Marginal Rate of Substitution measures how much of one good a consumer is willing to give up to get more of another.

Question 9

What is the graphical definition of the marginal rate of substitution (MRS)?

Answer 9

The MRS between good 1 and good 2 for a given bundle is equal to the negative slope of the indifference curve passing through that bundle.

Question 10

How is MRS represented graphically?

Answer 10

MRS is the negative of the slope of the indifference curve at a point.
Example: If the slope is −3, then MRS = 3.

Question 11

Calculate MRS if Δx2 = − 4 and Δx1=2 ​

Answer 11

Slope= Δx 2/ ​ Δx 1 ​

So, MRS = ∣ Slope ∣ = 2
MRS=∣Slope∣=2

MRS = 2

Question 12

What does a steeper indifference curve indicate about MRS?

Answer 12

The steeper the indifference curve, the higher the MRS. This means that the consumer is willing to give up a large amount of good 2 to obtain more of good 1.

Question 13

MRS?

Answer 13

The MRS measures how much of one good a consumer is willing to give up in order to obtain more of another good.

This trade-off is determined solely by preferences; utility values do
not matter.

In particular, the MRS remains unchanged if we use a different utility
function that represents the same preferences.

Question 14

MRS function?

Answer 14

MRS = MU1 / MU2 = ∂u/∂x1 / ∂u/∂x2

Question 15

MUi ?

Answer 15

The MUi depends on the utility function used to represent preferences.

Since the choice of utility function is arbitrary, the value of MUi alone is not informative. (If we use a new utility function where all utility
values are doubled, the marginal utility would also double.)

However, marginal utility can be useful because it allows us to compute the marginal rate of substitution.