WEEK 1- Consumer Theory- Preferences and Utility

Question 1

What are the axioms/assumptions behind preferences and utility in general (behind the theory)?

Answer 1

i) People are rational thinkers
ii) The theory doesn’t say consumers think in terms of consumer maximising theory just happens that way
iii) The theory is an approximation
iv) For situations where the theory is N/A we can use behavioural economics

Question 2

What are the axioms of consumer theory?

Answer 2

1) All bundles can be compared
2) All bundles can be ranked consistently
3) Similar bundles should have similar rankings
4) More is better
5) Averages preferred to extremes

Question 3

What are the axioms needed for the Preference of Bundles?

Answer 3

Axiom 1: COMPLETENESS (All bundles can be compared)
(For Bundles A and B: Either A is weakly preferred to B or vice versa)

Axiom 2: TRANSIVITY (All bundles can be ranked consistently)
i.e For bundles A,B,C: If A preferred to B and B to preferred to C. Then A preferred to C

IF A1 AND A2 HOLD THEN PREFERENCE ORDER EXISTS

Axiom 3: CONTINUITY (Similar Bundles have similar rankings)
For all bundles A, B and C: If A is strictly preferred to B and B is ‘close’ to C, then A
is (weakly) preferred to C

Axiom 4: MONOTONICITY (More is preferred to less)
For all bundles A and B: If A has more of both goods than B, then A is strictly
preferred to B

Axiom 5; CONVEXITY (Average preferred to extremes)

Question 4

What are the properties of Indifference Curves?

Answer 4

An indifference curve passes through every possible bundle

Indifference Curves downward sloping (NO POSITIVE GRADIENT)

Indifference Curves are bowed toward origin and convex to origin

Indifference Curves cannot cross

Indifference curves cannot be too ‘thick’

Question 5

Why is the property of being convex to the origin so important?

Answer 5

Displays ‘weakly preferred sets’
- Anything on the Indif line and above counts

• Important because if convex to origin then can pick two points anywhere on graph and draw straight line and won’t cross (SEE DIAGRAM IN NOTES)

Question 6

What is the Marginal Rate of Substitution (MRS)?

Answer 6

How much willing to give up one good to get extra unit of another

• Its gradient of Indif curve
• If convex to origin can see diminishing MRS (IF TRUE PREFER AVERAGES TO EXTREMES) (SEE DIAGRAM IN NOTES)

Question 7

How is a utility function given as?

Answer 7

U(X,Y)= U (bar)

Question 8

How can we define the marginal utility of good X?

Answer 8

Increase in good X while holding Y constant
(Denoted as MUx = Derivative of U/Derivative of X)

Vice Versa for Y:
(Denoted as MUy = Derivative of U/Derivative of Y)

Question 9

How do we calculate the MRS (Gradient of Indif Curve)?

Answer 9

dY/dX = - MUx/MUy (MATHS IN NOTES)

Question 10

What are some special forms of Indif Curves?

Answer 10

Perfect Substitutes (U = aX + bY
where a and b are constants)

Perfect Complements
U = min{X,Y}

Quasi-Linear Preferences
U = u(X) + Y

SEE Y1 NOTES FOR THE GRAPHS