Comprehensive summaries of the University of Oxford Microeconomics lecture notes, with supplementary readings included in the notes (predominately from Gravelle & Rees)
Preferences and Rationality
Consumers decide about bundles x , y ∈ X where X is closed, convex set ∈ R k ≥ 0
Preferences written x ≽ y ie x at least as good as y / weakly preferred x ≽ y ⇔ u ( x ) >u ( y )
Axioms of Rational Preferences
1. Complete: ∀ x , y ∈ X , either x ≽ y or y ≽ x or both (ie x ∼ y )
2. Reflexive: ∀ x ∈ X , x ≽ x
3. Transitive: ∀ x , y , z ∈ X , if x ≽ y and y ≽ z, then x ≽ z
4. Continuous: ∀ y ∈ X , the sets { x : x ≻ y } and { x : y ≻ x } are open ie every point contains a
neighbourhood
Conditions on Preferences
1. (Strict) monotonicity: if x ≥ y and x ≠ y then x ≽ y
a. The more the better
2. (Local) non-satiation: given any x ∈ X and any ε > 0, there is some bundle y ∈ X with
||x− y||<ε such that y ≻ x
a. Can always find a nearby bundle that would increase utility – utility doesn’t peak,
indifference curves are thin ⇒ non-satiation – means it can't be efficient to have total
consumption less than total output
3. (Strict) convexity: ∀ x ≠ y , z ∈ X , if x ≽ z and y ≽ z, then tx+ ( 1−t ) y ≻ z ∀ 0<t< 1
a. Averages are strictly preferred to extremes
Pareto Efficiency
Allocation x Pareto dominates x’ if everyone weakly prefers x to x’ and at least one agent
strictly prefers x to x’
Weakly Pareto efficient if no x ' s . t . x ' ≻ x ∀ i; strongly if no x ' s . t . x ' ≽x ∀ i and x ' ≻ x for
at least one i – two coincide under continuous, monotonic preferences
Allocation is Pareto efficient if not Pareto dominated – can't make anyone better off w/o
making someone worse off
Allocations can be Pareto efficient, eqba aren’t as include a price vector too – nonsensical
An optimal allocation is a feasible allocation with the property that there is no other feasible
allocation which is ranked higher by the welfare preference ordering
Paretian Value Judgements
Process independence: the process by which a particular allocation is achieved does not
matter – ie don’t care if people make their own decisions or if a social planner tells them what
to do
Individualism: only aspect of an allocation which is relevant is its effect on utilities of the
individuals in the society
Non-paternalism: allocations are evaluated by reference to individuals’ own utility functions
means it is assumed that individuals are the best judges of their own welfare – strong
assumption eg wouldn’t respect individuals’ decisions on drug consumption
Benevolence: benevolent in that a ceteris paribus increase in utility of one individual is
judged to be an improvement – making rich richer without making poor poorer is an
improvement – poor don’t spite the rich becoming richer so their own utilities are unchanged
o Implies indifference curves negatively sloped
Issues with Pareto Efficiency
Weak criterion, can't Pareto compare all outcomes, doesn’t refer to distribution of income
Process independence, individualism, non-paternalism, benevolence
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