Week 1 Term 1

Question 1

What is Consumption Set?

Answer 1

a set which belongs to the non-negative space and has n goods

Question 2

How many are the axioms of preference and what are they?

Answer 2

They are five - monotonicity, completeness, transitivity, continuity, convexity

Question 3

What is monotonicity?

Answer 3

if one bundle contains at least as much of every commodity as another bundle. then the one is at least as good as the other, thus it is strictly better if it contains strictly more of every good - MORE IS BETTER

Question 4

what is completeness?

Answer 4

any two bundles can be compared (better, worse, same)

Question 5

what is transitivity?

Answer 5

Question 6

what is continuity?

Answer 6

it ensures there are no sudden jumps in preferences; makes the existance of IC possible

Question 7

what is convexity?

Answer 7

averages are preferred to extremes;

Question 8

If all 5 axioms are satisfied, how can utility functions be represented?

Answer 8

through IC whose level sets are nonintersecting, strictly convex away from the origin, with higher indifference curves depicting higher levels of utility

Question 9

What is the Continuity Axiom Violation ?

Answer 9

aka Lexicographic preferences; cannot be represented on IC diagrams - know proof!

Question 10

What is MRS?

Answer 10

stands for marginal rate of substitution; it is the slope of the IC; is also (rise over run)

Question 11

Consumer’s UMP (Utility Maximisation Problem)

Answer 11

most important: slope of the budget constraint = slope of the IC, since IC tangential to BC.

Question 12

Properties of Marshallian Demands

Answer 12

• x* (p,m) is continuous in prices (p) and income (m)
• it is also HOMOGENEOUS of degree 0 in prices (p) and income (m)
• it is also differentiable in prices (p) and income (m)

Question 13

what does homogeneity mean in certain variables ?

Answer 13

changing all prices and income in the marshallian demands by a common mutliple , does not change the marshallian demands.

Question 14

What is an indirect utility function?

Answer 14

• it is a function of both commodity price and income
• it is the relationship between prices, income and the maximised value of utility
• the level of utility achieved when x* is chosen is the highest level permitted by the consumer’s BC facing prices pi and income m.

Question 15

What does the Indirect Utility Function give?

Answer 15

it gives the maximum level of utility that can be achieved when facing prices p and income m.

Question 16

What are the properties of IUF?

Answer 16

• v (p, m) is continuous in prices (p) and income (m)
• v (p, m) is strictly increasing in income (m) and decreasing in prices (p) - proven with FOCs
• it is homogenous of degeree 0 in prices (p) and income (m)

Question 17

What is Roy’s Identity?

Answer 17

• the negative ratio between foc p1 and foc m results in marshallian demand 1

Question 18

When are preferences strictly convex?

Answer 18

• when all mixtures of z = (x + y)/ 2 are strictly preferred to their component bundles x and y

Question 19

What are non-convex preferences?

Answer 19

• when the mixture z = (x+y) /2 is less preferred than x or y

Question 20

what are well-behaved preferences?

Answer 20

Preferences which are monotonic and convex.

Question 21

what is a well behaved utility function?

Answer 21

one that is continuous, strictly increasing, and strictly quasi-concave

Question 22

What is strict quasi-concavity?

Answer 22

• if we take any two points in a domain and form any convex combination of them, the value of the function must be higher than the lowest value it takes at the two chosen points

Question 23

What is the difference between strict quasi-concavity and increasing function vs strict quasi-concavity and decreasing function?

Answer 23