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: APL=q/L

Marginal productivity: MPL=dq/dL

Ave prod. falls when MPL<APL

MPL falls, eventually (the „law” of diminishing marginal productivity)

Isoquants

All combinations of factors that allow same production

Stolen from: prenhall.com

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

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.

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

Cost minimization

Cost minimization with fixed production

Dual problem to maximizing production with fixed costs

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

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

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)

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+bq2

MR=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

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

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

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

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)

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

left middle

right

up 2,2 4,1 1,3

down

6,1 2,5 2,2

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?

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)

Low price

High price

Low price

1,1 3,0

High price

0,3 2,2

„prisoner’s dillema”

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

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

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

Oligopoly: Stackelberg

First player (Leader) decides on quantity Follower react to it SPNE found using backward induction:

Π2=q2(a-b(q1+q2))-TC2

Reaction curve as in Cournot:q2= (a-bq1-MC2)/2b

For constant MC we get: q1 =2q2 =(a-MC)/2b

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

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

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=9q2 q1=12-P2+P1

P1=P2=10>MC

Before the exam

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