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