Summary almost everything you need to know about

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

Production functions u Q=f(K, L) u Short run: at least one factor fixed u Long run: anything can change u Average productivity: APL=q/L u Marginal productivity: MPL=dq/d. L u Ave prod. falls when MPL<APL u MPL falls, eventually (the „law” of diminishing marginal productivity)

Isoquants u All combinations of factors that allow same production Stolen from: prenhall. com

Substitution u MRTSKL=-MPK/MPL u (how many units of labor are necessary to replace one unit of capital) u MRTS is the inverse of the slope of the isoquant

Economies of scale u f(z. K, z. L)><=zf(K, L), z>1 u Shows whether large of small production scale more efficient u Example: Cobb-Douglas: u (z. K)α(z. L)β=z(α+β)KαLβ u Thus economies of scale are constant (increasing, decreasing) if α+β equal to (greater than, smaller than) 1.

Costs u Economist’s and accountant’s 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)=d. TC(q)/dq u MC assumed to go up, eventually u AVC(q) and ATC(q) minimum when equal to MC

Cost minimization u Cost minimization with fixed production u Dual problem to maximizing production with fixed costs

Perfect competition u 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 „pricetaker”) – Profit maximisation – Decreasing economies of scale Main feature: perfectly elastic demand for a single firm

Perfect competition-analysis u Magical formula: MC(q)=P u Defines inverse supply f. for a single firm u Aggregate supply: S(P)=ΣSi(P) u In the long run: – Profit=0 – P=min(AC) – S=D u Efficiency: – Lowest possible production cost – Production level appropriate given preference

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)

Monopoly-cont’d u u u u By increasing production, monopoly negatively affects prices Thus MR lower than AR(=p) E. g. with P=a+bq: TR=Pq=(a+bq)q=aq+bq 2 MR=a+2 bq Another useful formula: link with demand elasticity: MR=P(q)(1+1/ε) Thus always chooses such q that demand is elastic Inefficiency: production lower than in PC, price higher – deadweight loss Plus, losses due to rent-seeking

Monopoly: price discrimination u Trying to make every consumer pay as much as (s)he agrees to pay u 1 st 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

Price discrimination-cont’d u 2 nd degree: different units at different prices but everyone pays the same for same quantity u Examples: mineral water, telecom. u 3 rd degree: different people pay different prices – (because different elasticities) – E. g. : discounts for students

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

Game theory u Used to model strategic interaction u Players choose strategies that affect everybody’s payoffs u Important notion: (strictly) Dominant strategy – always better than other strategy(ies)

Example left u Strategy middle right „left” is 2, 2 4, 1 1, 3 dominated by „right” up u Will not be played dow 6, 1 2, 5 2, 2 u up, down, middle and n 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

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 β?

Repeated games-cont’d „prisoner’s dillema” Low price High price Low price 1, 1 3, 0 High price u u u 0, 3 2, 2 Consider „trigger” stragegy: I play high but if you play low once, I will always play low. If you play high, you will get 2+2β+2β 2+… If you play low, you will get 3+β+β 2+… Collusion (high-high) can be sustained if our βs are. 5 or higher (though low-low also an equilibrium in a repeated game)

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

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

Cournot duopoly with linear demand u P=a-b. Q=a-b(q 1+q 2) u Cost functions: g(q 1), g(q 2) u Π 1=q 1(a-b(q 1+q 2))-g(q 1) u Optimization yields q 1=(a-bq 2 MC 1)/2 b 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)/3 b

Oligopoly: Stackelberg u First player (Leader) decides on quantity u Follower react to it u SPNE found using backward induction: Π 2=q 2(a-b(q 1+q 2))-TC 2 Reaction curve as in Cournot: q 2= (a-bq 1 -MC 2)/2 b u For constant MC we get: q 1 =2 q 2 =(a-MC)/2 b

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 v. S u Firm 2 will produce and earn less u Production higher, price lower in Stackelberg if cost and demand are linear

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 other’s cost

More realistic: heterog. goods u Competitor’s 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=9 q 1, TC 2=9 q 2 q 1=12 -P 2+P 1 P 1=P 2=10>MC

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