Term 1 week 1

Question 1

what would R^2 mean for notion?

Answer 1

All the conceivable consumption sets within the two good space.

Question 2

What is capital X?

Answer 2

X = the set of consumption bundles

Question 3

When using bundles and good what is the notation with sub and super scripts?

Answer 3

Super script is bundle, Sub script is good.

Question 3

If n=2 what can be a possible X = ?

Answer 3

X = {2 oranges and 1 apple}, {1 orange and 2 apples}.

Question 4

What is preference relation and what is important about it?

Answer 4

-Preference relation is the attitude to alternatives.

-MUST USE CURVED greater than or less than

-Curved greater than or equaled to is is at least as good.

Squiggly line means indifferent.

Question 5

What axiom of completeness?

Answer 5

(Can rank)
-Completeness: if two bundles x^1 and x^2 either x^1 is at least as good as x^2 or vice versa.

-You will have to be able to reflect preferences and cant shrug shoulders.

Question 6

What is the axiom of Transitivity?

Answer 6

If you prefer x^1 to x^2 and you prefer x^3 to x^2 then you must also perfer x^3 to x^1.

Question 7

What is the axiom of strict montonicity?

Answer 7

• More is better

if X^2 has at least as much of every commodity as X^1 then X^2 is at least as good as X^1.

-It is strictly preferred if it has more of every good.

Question 8

1. What is the axiom of continuity?
2. How would you explain it graphically?

3.What does this mean and imply?

Answer 8

1. If there is a sequence of bundles {xn) that tends to infinity and converges to bundle y.

If {xn is at least as good as z}

Then the bundle it converges to y is at least as good as z.

2. if you draw three bundles x1, x0 and xm. If x0 is preferred to x1 and xm is preferred to x0 and x1 and xm are connected then there will be a bundle on that connection that will be indifferent to x0.
3. This means that indifference curves can be drawn and there are no sudden jumps in perferences.

Question 9

1.What is the axiom for strict convexity?

2. What is the opposite of strict convexity?

Answer 9

1.- if you take a convex set of two bundles it is strictly better than the two bundles. (it lies on higher indifference curve)

2. if preferences are non - convex a convex set of two bundles lies on a lower indifference curve than the two bundles.

Question 10

What are the 5 axioms required to present something as a real valued utility function?

Answer 10

• Completeness
• Transitivity
  -Strict monotonicity
  -Continuity
  -Strict convexity

Question 11

What are the features of a U(.) utility function?

Answer 11

• Continuous
• Strictly increasing
• Strictly quasiconcave
  -Any monotonic transformation will preserve utility ranking

Question 12

What is the difference between strict convexity and convexity?

Answer 12

• Strict convexity, we see the downward sloping IC = substitute goods

-Just Convexity we see linear like perfect substitutes, perfect complements.

Question 13

What is the relationship between quasi-concavity and indifference curves?

Answer 13

• Strict convexity makes strict quasiconcavity

-Convexity makes quasi- concave.

Question 14

What is quasi-concavity?

Answer 14

-If the better set is concave

-Goes for increasing and decreasing functions.

Question 15

1.What are lexiographic preferences?

2. What is particular about them?

Answer 15

1.-When you have a liking for one good.
-You will always choose the bundle that has more of that 1 good

Eg x^1 {1 apple and 3 oranges}
x^2 {2 apple and 2 oranges}

You will always go for x^2 as it has more apples even tho less oranges.

2. They violate continuity and hence indifference curves cannot be drawn.

Question 16

Why do lexiographic preferences violate continuity?

Answer 16

Assume you have sequence {x^n} = {1/n, 0} and y = {0,0} and z = {0,1}
as {x^n} tends to infinity xn converges to y. However, z is preferred to y.

Question 17

What is the utility maximisation problem?

How do you do it?

What do you get from it?

Answer 17

You maximise utility subject to a budget constraint.

You use the lagrange method

You get x* which are the marshallian demands.

Question 18

what is pi and xi

What is the budget set?

Answer 18

pi is price of good i, xi is quantity of good i

All feasible combinations of two goods?

Question 19

What can / may the lagrange not be used for UMP?

Answer 19

• Cannot be used for perfect complements due to discontinuity
  -For perfect substitutes we compare slope of BC and IC as there will be multiple equilibria, to find which corners solution will be.

Question 20

What is an important step for setting up the lagrange?

Answer 20

Lets say m = p1x1+p2x2
before the L to make a +
it needs to be m - p1x1 - p2x2.
+ L [m-p1x1-p2x2].

Question 21

Graphically what is the UMP?

Answer 21

Where BC is tangent to IC

MRS = Price ratio

Question 22

How do you calculate Price ratio?

How do you calculate MRS?

Answer 22

-p1/p2

-MU1/MU2

Question 23

What are the steps to solving the lagrange?

Answer 23

Write out with L

-Differentiate with respect to x1, x2 and L.
-Get rid of lamda
-Then use this combined to solve for x or y
-Then plug this into equation 3.
-Then solve for X in equation 3.

Question 24

What are the properties of marshallian demand function?

Answer 24

-x*(p,m) is continuous in prices and income

-x*(p,m) is homogenous of degree 0 in prices and income. Changing prices and income by common multiple does not change marshallian demand

-x*(p,m) is differentiable in prices and income.

Question 25

What can you get with the marshallian demands?

What else can you do?

Answer 25

• You can get the highest possible level of utility

-You get the indirect utility function

Question 26

What is indirect utility function?

Answer 26

This is when you get the marshallian demands and you put them into the utility function.

-Gives you the relationship between: prices, income and utility.

Question 27

what are the properties of the Indirect Utility Function?

How can you prove the second property?

Answer 27

-V(p,m) Continuous in prices and income
-V(p,m) is strictly increasing in income and strictly decreasing in prices.
dv/dm> 0
dv/dp<0
-It is homogenous of degree 0 in prices and income.

-If it is differentiable it satisfies roy’s identity.

Question 28

What is Roy’s identity?

What is something to remeber

Answer 28

if you take IUF

the - (dv/dp1)/(dv/dm) = marhallian demand for good 1.

REMEMBER NEGATIVE IN FRONT!