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

Summary (almost) everything you need to know about micro theory in 30 minutes. Production functions. Q=f(K,L) Short run: at least one factor fixed Long run: anything can change Average productivity: AP L =q/L Marginal productivity: MP L =dq/dL Ave prod. falls when MP L <AP L

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

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

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

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

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

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

  6. Costs • Economist’s and accountant’s view • Opportunity costs • Sunk costs („bygones are bygones”) • TC(q)=VC(q)+FC • ATC(q)=TC(q)/q • MC(q)=dTC(q)/dq • MC assumed to go up, eventually • AVC(q) and ATC(q) minimum when equal to MC

  7. Cost minimization • Cost minimization with fixed production • Dual problem to maximizing production with fixed costs

  8. Perfect competition • 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 • Main feature: perfectly elastic demand for a single firm

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

  10. Monopoly • Sources of monopolistic power • Administrative regulations (e.g. Poczta Polska) • Natural monopoly (railroad networks) • Patents • Cartels (the OPEC) • Economies of scale • The magic formula: MR(q)=MC(q)

  11. Monopoly-cont’d • 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+bq2MR=a+2bq • 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

  12. Monopoly: price discrimination • Trying to make every consumer pay as much as (s)he agrees to pay • 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

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

  14. Two-part tarifs • Access fee + per-use price • Examples: Disneyland, mobile phones, vacuum cleaners • Homogenous consumers: • Fix per-use price at marginal cost • Capture all the surplus with the access fee • Different consumer groups • Capture all the surplus of the „weaker” group • Price>MC • OR: forget about the „weaker” group altogether

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

  16. Example • Strategy „left” is dominated by „right” • Will not be played • up, down, middle and right are rationalizable • Nash equilibrium: two strategies that are mutually best-responses (no profitable unilateral deviation) • No NE in pure strategies here • NE in mixed strategies to be found by equating expected payoffs from strategies

  17. Repeated games • Same („stage”) game played multiple times • If only one equilibrium, backward induction argument for finite repetition • What if repeated infinitly with some discount factor β?

  18. Repeated games-cont’d • 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+2β2+… • If you play low, you will get 3+β+β2+… • Collusion (high-high) can be sustained if our βs are .5 or higher • (though low-low also an equilibrium in a repeated game) „prisoner’s dillema”

  19. Sequential games • A tree (directed graph with no cycles) with nodes and edges • Information sets • Subgame: a game starting at one of the nodes that does not cut through info sets • SPNE: truncation to subgames also in equilibrium • Backward induction: start „near” the final nodes • Example: battle of the sexes

  20. Oligopoly: Cournot • Low number of firms • Firms not assumed to be price-takers • Restricted entry • Nash equilibrium • Cournot: competition in quantities • Example: duopoly with linear demand

  21. Cournot duopoly with linear demand • P=a-bQ=a-b(q1+q2) • Cost functions: g(q1), g(q2) • Π1=q1(a-b(q1+q2))-g(q1) • Optimization yields q1=(a-bq2-MC1)/2b • (reaction curve of firm 1) • Cournot eq. where reaction curves cross • Useful formula: if symmetric costs:q1 =q2 =(a-MC)/3b

  22. Oligopoly: Stackelberg • First player (Leader) decides on quantity • Follower react to it • SPNE found using backward induction:Π2=q2(a-b(q1+q2))-TC2Reaction curve as in Cournot:q2= (a-bq1-MC2)/2b • For constant MC we get: q1 =2q2 =(a-MC)/2b

  23. Comparing Cournot and Stackelberg • Firm 2 reacts optimally to q1 in either • But firm 1 only in Cournot • Firm 1 will produce and earn more in vS • Firm 2 will produce and earn less • Production higher, price lower in Stackelberg if cost and demand are linear

  24. Oligopoly: plain vanilla Bertrand • Both firms set prices • Basic assumption: homogenous goods • (firm with lower price captures the whole market) • Undercutting all the way to P=MC • If firms not identical, the more efficient one will produce and sell at the other’s cost

  25. More realistic: heterog. goods • Competitor’s price affects my sales negatively • (but not drives them to 0 when just slightly lower than mine) • Example:q1=12-P1+P2 TC1=9q1, TC2=9q2q1=12-P2+P1P1=P2=10>MC

  26. Before the exam • Look up www.miq.woee.pl (password: miq) for questions, tests and more

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