Cheat sheet Micro PDF

Title Cheat sheet Micro
Course Microeconomics
Institution University of Melbourne
Pages 14
File Size 1.2 MB
File Type PDF
Total Downloads 133
Total Views 307

Summary

Utility Function: Imaginary ObjectCriticism: They do not exist in real life The Choice Set: o Including goods you care about o Excluding goods do not care about Preferences  Choice set is a collection of bundles i. x and y (bold means vectors) o x≽ y: an individual finds x at least as good as y (or...


Description

Utility Function: Imaginary Object Criticism: They do not exist in real life The Choice Set: o Including goods you care about o Excluding goods do not care about Preferences  Choice set is a collection of bundles i.e. x and y (bold means vectors) o x≽ y: an individual finds x at least as good as y (or weakly prefers x to y) o x∼ y :an individual is indifferent between x and y o x≻ y : an individual strictly prefers x to y Assumptions: 1. Completeness= any two bundles x and y can be compared 2. Transitivity= if bundle x is at least good as y and y is at least as good as bundle z, then x is at least as good as z  Preferences must be transitive to make sense 3. Monotonicity= If two bundles x and y are such that bundle y contains more of each good than bundle x (denoted y ≫x then an individual prefers y to x ( y ∼ x) 4. G-Continuity=for any two bundles with positive goods (x>>0) there exists a nonnegative real number such that a ∙ x ∼ y  G-continuity rules out two things: o y is better than a ∙ x NO matter how large a is o Your choice “jumps” i.e. y ≻ x BUT x≻ a∙ y for any au(z)=u(t)>u(y)=u(x) Positive Monotonic Transformation: Any positive monotonic transformation of utility fiction will represent same preferences  WHY? Only care about how two numbers compare Altruistic behaviour, motivation & standard model: Selfish Behaviour: Economist criticised that assume selfish behaviour, look at a concrete example:

o Agent 1 given $5 to allocate between agent 1 and agent 2 Alternative Models  Number of theories that model this in more detail -> rationalise “giving” 1. u FS (x,y)=x-δ|x−y| where 00 ∂Y

∂ q 0 - Giffen: when demand increases as price increases ∂p ∂q 0

0 or 0

Giffen Experiment: -

Max 3 spots, new red line (solution must be under 2) Old Slope line Point

Game Theory Defining formal strategic games:  A formal game consists of: o A set of players: i=1,2… N o A set of pure strategies (or actions) for each player i→ Si={s a , s b ,… s m } o A vector of strategies for all players s=(s1 ,… sN) where each si corresponds to a pure strategy of player i  Called a strategy profile  Vector determines what each player has done and determines the outcome of the game o A payoff (or utility) function, ui (s) for each player i and every strategy profile, s  Notation: s−i : strategy profile that excludes i’s pure strategy Strictly Dominant Strategies:

Strictly Dominated Strategies:

PSNE: A strategy profile s* ∈ S is a pure strategy Nash equilibrium (PSNE) if no player can gain by using some other strategy - If multiple NE, the most efficient won’t necessarily be chosen Best Response: Eg. BRA(l)=L MSNE: - Can be symmetric and asymmetric

Representing Best Responses Graphically:

Congestion Games

- When testing for NE eg (say LH, hsH and hl) - Do probability p, q, and 1-p-q Government Intervention

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Utilities are negative, so highest utility is lowest travel time

Mixed Strategy NE - Find PSNE Then asymmetrical

Political Competition

Deterministic Winning (DW): - Care about winning (Doesn’t matter by how much)

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Ie if a=0.5 and b=0.8, a definitely wins

Probabilistic Winning (PW) - a=1-b 50% chance of winning

Deterministic Position (DP) - Suppose that party 0 is located at a < 1/2. - Where party 1 locate? As close to 1, but ensuring the win: at b = 1 − a − 0.01.

Probabilistic Position (PP)

Game Theory: Sequential Games Game Tree

Tutorial Example

With Punishment:

How To Solve=Backward Induction - Last branch First Subgame (SPNE)

Information Sets The idea that a player does not know what happened earlier in the game; or, in a more formal language, a player cannot distinguish histories of the game

Bertrand vs Cournot -

Bertrand= Prices Cournot= Quantity Max Profit (PxQ) with respect to p (bert) and q (Cournot) If there are costs p=1-q-c

Alpha - How many people search for the lowest price

Search Costs - taste parameter x ∈ [0, 1]; - α measures how different the products are. If α = 0, then two products are identical. - Total cost =Price + Disutility eg (p0+ αx if from firm 0), p1 + α(1 − x) if buying from Frim 1.

Recycling and Information Cascades -

Remember when doing 3rd player, they must infer the actions of the second player

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Compare to the probability of it being a G or R day

Bilateral Trade -

How much buyer and seller value Want all efficient trades to go through Seller Makes an Offer (0,0.1) is efficient but will not happen as offers price of 1 Buyers can make offers

For Sellers:

For Buyers

SPNE:

Prices

Extra Maths Notes...


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