Consumer Theory II

Question 1

What does the Utility Function, U(x, y), imply?

Answer 1

It implies the Consumer only cares about Goods x and y, nothing else
-Both Goods must be consumed to gain Utility

Question 2

Denote the Price of x + the Price of y

Answer 2

Price of x = Px

Price of y = Py

Question 3

What is the Budget Constraint equation?

Answer 3

Budget = Px(x) + Py(y)

Question 4

What is the MRS and how do you calculate it?

Answer 4

MRS- Marginal Rate of Substitution shows the Slope of the Indifference Curve
MRS = dy/dx

Question 5

At the Optimum Consumption Bundle, what is the Slope of the Budget Constraint equal to?

Answer 5

MRS

Question 6

how do you find the optimum level of Consumption for goods x and y?

Answer 6

Find the Slope of the Budget Constrain (B.C)-
—dU = ydx + xdy = 0
Equate MRS and Slope of B.C, MRS = Slope
Rearrange in terms of y and Sub. back into B.C

Question 7

What does Marginal Utility tell us?

Answer 7

It tells us What the Gain in Utility is if we Increased Consumption of the Good by a small amount

Question 8

What happens to Utility if you change the amount of each Good you Consume?

Answer 8

You can Consume different amounts of the Goods, BUT you Stay on the SAME Indifference Curve
So, Change in Utility, dU, is 0

Question 9

What do you use to find the Total Change in Utility?

Answer 9

Partial + Total Derivatives

Question 10

What does [dU(x, y) / dx] x dx show?

Answer 10

dU if x changes (a little), keeping y constant

Marginal Utility of x

Question 11

What does [dU(x, y) / dy] x dy show?

Answer 11

dU if y changes (a little), keeping x constant

Marginal Utility of y

Question 12

What is the Equation for the Total Change in Utility?

Answer 12

dU(x, y) = Marginal Utility of x dx + Marginal Utility of y dy
dU(x, y) = [dU(x, y) / dx] x dx + [dU(x, y) / dy] x dy
dU(x, y) = MUx dx + MUy dy

Question 13

Given that you remain on the same Ic, show that the Change in Utility = -MUx/MUy

Answer 13

dU(x, y) = MUx dx + MUy dy
If you remain on same Ic--> Change in Utility = 0
=> dU(x, y) = 0=> 0 = MUx dx + MUy dy
=>MUx dx = -MUy dy
dy/dx = MRS = -MUx/MUy

Question 14

If Income Increases, what happens to the Ic for a Normal Good?

Answer 14

B.C + Ic Shift Outwards- to the Right

Can Consume more of Both Goods

Question 15

If Income Increases, what happens to the Consumption of an Inferior Good?

Answer 15

B.C Shifts Outwards- to the Right
Ic Shifts Left- But is on NEW B.C
—Consume less of Good x (Inferior Good)
Consume more of y and less of x

Question 16

What are the 2 effects on the Law of Demand?

Answer 16

Income + Substitution effects

Question 17

What happens to the B.C if the Price of Good x falls?

Answer 17

B.C rotates about Py- M/Px moves along x axis

Question 18

What does a Change in the Price of a Good cause?

Answer 18

Change in Choice of Consumption

Question 19

What does Px/Py show?

Answer 19

How expensive Good x is relative to Good y

Tells us our Incentive to Substitute x for y- e.g. Increase x + Decrease y

Question 20

What does M/Px tell us?

Answer 20

Tells us Income in REAL Terms of Good x
-Shows how our Income Changes
Fall in Price of Good x–> Increase REAL Income in terms of Good x

Question 21

How does a fall in the Price of x of a Normal Good affect the B.C + Ic? Explain effects of Income + Substitution effects

Answer 21

Fall in Price of x–> M/Px moves along x axis
Intermediate Step: Line Tangent to Ic1 but parallel to B.C2
–Where this line is a Tangent to Ic1- shows Consumption after impact of Substitution effect
Where B.C2 is tangent to Ic2- shows final Consumption + Income effect from Intermediate Step

Question 22

What does the Substitution effect depend on?

Answer 22

Depends ONLY on Price Change

Question 23

What does the Income effect depend on?

Answer 23

Depends ONLY on fact REAL Income Increases

Question 24

For an Inferior Good, which out of the Substitution + Income effects is Positive + Negative?

Answer 24

Substitution- POSITIVE

Income- Negative

Question 25

What are Giffen Goods?

Answer 25

Goods where Consumption Increases as Price Increases

Question 26

Why may Price Increases lead to Increased Consumption?

Answer 26

Increased Price may mean Increased Quality

e.g. iPhone

Question 27

What happens to the B.C with Increased Cash compared to Free Goods?

Answer 27

Cash- Shifts B.C Outwards completely
Free Goods- Shift B.C Out by value of Free Good ONLY for Good it is applicable to
If Free Good for Good x is worth 5- M/Py remains same, M/Px–> M/Px + 5

Question 28

What is the Utility Function of Goods consumed together, e.g. Left + Right Glove, and what is the Shape of the Ic?

Answer 28

min{x, y} = x + y

Ic at Right Angles