# Summary (almost) everything you need to know about micro theory in 30 minutes

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- Slide 1
- Summary (almost) everything you need to know about micro theory in 30 minutes
- Slide 2
- Production functions u Q=f(K,L) u Short run: at least one factor fixed u Long run: anything can change u Average productivity: AP L =q/L u Marginal productivity: MP L =dq/dL u Ave prod. falls when MP L
- Economies of scale u f(zK,zL)> 1 u Shows whether large of small production scale more efficient u Example: Cobb-Douglas: u (zK) (zL) =z(+)K L u Thus economies of scale are constant (increasing, decreasing) if + equal to (greater than, smaller than) 1.
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- Costs u Economists and accountants view u Opportunity costs u Sunk costs (bygones are bygones) u TC(q)=VC(q)+FC u ATC(q)=TC(q)/q u MC(q)=dTC(q)/dq u MC assumed to go up, eventually u AVC(q) and ATC(q) minimum when equal to MC
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- Cost minimization u Cost minimization with fixed production u Dual problem to maximizing production with fixed costs
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- Perfect competition u Assumptions Many (small) firms New firms can enter in the long run Homegenous product Prices known No transaction or search costs Prices of factors (perceived as) constant Market price perceived as constant (firm is a price- taker) Profit maximisation Decreasing economies of scale u Main feature: perfectly elastic demand for a single firm
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- Perfect competition-analysis u Magical formula: MC(q)=P u Defines inverse supply f. for a single firm u Aggregate supply: S(P)=S i (P) u In the long run: Profit=0 P=min(AC) S=D u Efficiency: Lowest possible production cost Production level appropriate given preference
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- Monopoly u Sources of monopolistic power Administrative regulations (e.g. Poczta Polska) Natural monopoly (railroad networks) Patents Cartels (the OPEC) Economies of scale u The magic formula: MR(q)=MC(q)
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- Monopoly-contd u By increasing production, monopoly negatively affects prices u Thus MR lower than AR(=p) u E.g. with P=a+bq: TR=Pq=(a+bq)q=aq+bq 2 MR=a+2bq u Another useful formula: link with demand elasticity: MR=P(q)(1+1/) u Thus always chooses such q that demand is elastic u Inefficiency: production lower than in PC, price higher deadweight loss u Plus, losses due to rent-seeking
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- Monopoly: price discrimination u Trying to make every consumer pay as much as (s)he agrees to pay u 1st degree (perfect price disc. every unit sold at reservation price), production as in the case of a perfectly competitive market (thus no inefficiency) No consumer surplus either
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- Price discrimination-contd u 2nd degree: different units at different prices but everyone pays the same for same quantity u Examples: mineral water, telecom. u 3rd degree: different people pay different prices (because different elasticities) E.g.: discounts for students
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- Two-part tarifs u Access fee + per-use price u Examples: Disneyland, mobile phones, vacuum cleaners u Homogenous consumers: Fix per-use price at marginal cost Capture all the surplus with the access fee u Different consumer groups Capture all the surplus of the weaker group Price>MC OR: forget about the weaker group altogether
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- Game theory u Used to model strategic interaction u Players choose strategies that affect everybodys payoffs u Important notion: (strictly) Dominant strategy always better than other strategy(ies)
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- Example u Strategy left is dominated by right u Will not be played u up, down, middle and right are rationalizable u Nash equilibrium: two strategies that are mutually best-responses (no profitable unilateral deviation) u No NE in pure strategies here u NE in mixed strategies to be found by equating expected payoffs from strategies leftmiddl e right up2,24,11,3 dow n 6,12,52,2
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- Repeated games u Same (stage) game played multiple times u If only one equilibrium, backward induction argument for finite repetition u What if repeated infinitly with some discount factor ?
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- Repeated games-contd u Consider trigger stragegy: I play high but if you play low once, I will always play low. u If you play high, you will get 2+2+2 2 + u If you play low, you will get 3++ 2 + u Collusion (high-high) can be sustained if our s are.5 or higher u (though low-low also an equilibrium in a repeated game) Low price High price Low price 1,13,0 High price 0,32,2 prisoners dillema
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- Sequential games u A tree (directed graph with no cycles) with nodes and edges u Information sets u Subgame: a game starting at one of the nodes that does not cut through info sets u SPNE: truncation to subgames also in equilibrium u Backward induction: start near the final nodes u Example: battle of the sexes
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- Oligopoly: Cournot u Low number of firms u Firms not assumed to be price-takers u Restricted entry u Nash equilibrium u Cournot: competition in quantities u Example: duopoly with linear demand
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- Cournot duopoly with linear demand u P=a-bQ=a-b(q 1 +q 2 ) u Cost functions: g(q 1 ), g(q 2 ) u 1 =q 1 (a-b(q 1 +q 2 ))-g(q 1 ) u Optimization yields q 1 =(a-bq 2 - MC 1 )/2b u (reaction curve of firm 1) u Cournot eq. where reaction curves cross u Useful formula: if symmetric costs: q 1 =q 2 =(a-MC)/3b
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- Oligopoly: Stackelberg u First player (Leader) decides on quantity u Follower react to it u SPNE found using backward induction: 2 =q 2 (a-b(q 1 +q 2 ))-TC 2 Reaction curve as in Cournot: q 2 = (a-bq 1 -MC 2 )/2b u For constant MC we get: q 1 =2q 2 =(a-MC)/2b
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- Comparing Cournot and Stackelberg u Firm 2 reacts optimally to q 1 in either u But firm 1 only in Cournot u Firm 1 will produce and earn more in vS u Firm 2 will produce and earn less u Production higher, price lower in Stackelberg if cost and demand are linear
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- Oligopoly: plain vanilla Bertrand u Both firms set prices u Basic assumption: homogenous goods u (firm with lower price captures the whole market) u Undercutting all the way to P=MC u If firms not identical, the more efficient one will produce and sell at the others cost
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- More realistic: heterog. goods u Competitors price affects my sales negatively u (but not drives them to 0 when just slightly lower than mine) u Example: q 1 =12-P 1 +P 2 TC 1 =9q 1, TC 2 =9q 2 q 1 =12-P 2 +P 1 P 1 =P 2 =10>MC
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- Before the exam u Look up www.miq.woee.pl (password: miq) for questions, tests and morewww.miq.woee.pl

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