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FHS > Microeconomics > Flashcards

Microeconomics Flashcards

1
Q

Competitive equilibrium definition and assumptions

A

Def: is (x,p) s.t. MRSa= MRSb = p/p and wa + wb = xa + xb
- must specify price and allocation

Assumptions: continuous, convex, monotonic consumer preferences. w>0

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2
Q

Walrus’ law

What does it imply

A

p1z1 + p2z2 = 0

Excess demand: z = xa - wa + xb - wb

In general equilibrium model with 2 goodS: if one market clears so does the other. Need income = profit.

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3
Q

Assumptions of production economy (competitive equilibrium)

A

no increasing returns
free disposal
irreversibility of production
wages & prices are competitive

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4
Q

Trade model

A

Hecksher-Ohlin:

  • Assumes LOOP
  • direction of trade is irrelevant for improving customer’s utility if the customers in the 2 countries are identical. If different one country could be worse off
  • Autarky -> gains from trade (substitution shift) -> gains from specialisation (income shift)
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5
Q

Stopler-Samulseon

A

If CRS and both goods continue to be produced, a relative increase in the price of a good will increase the real return to the factor used intensively in that industry and reduce the real return to the other factor

  • some producers can suffer from trade liberalisation
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6
Q

Equity in efficiency

A

Amartya Sen: ‘an economy can be Pareto-optimal and still be perfectly disgusting’
- optimal if can’t make starters better off w/o cutting into the rich

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7
Q

Second theorem of welfare economics

A

if (x,y,p) is competitive equilibrium then (x,y) is pareto efficient (x,p) and (l,w) then (x,l) = (2,1) PE

If fixes prices and have any w on BC then agents will trade to x*

Assuming that preferences and production sets are
convex, any Pareto efficient allocation can be achieved as a GCE with appropriate initial endowments (i.e. can be achieved via lump-sum transfers)

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8
Q

Social welfare functions

A

Utilitarian: sum utilities
- unit comparable (differences) and cardinality
- to rank allocations that aren’t Pareto comparable need to compare loss of one with gain of another
Rawlsian: maxmin
- level comparable (total)
- if agents have same preferences then can be ranked (don’t need cardinality)

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9
Q

Define strategyproofness

A

no agent can report different preferences and be better off under the outcome of the social welfare function

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10
Q

Arrow’s impossibility theorem

A

No social rule that satisfies these 4 axions:

U - unrestricted domain
- single-peaked preferences (one-dimensional alternatives)
P - pareto optimal
I - irrelevance or independent alternatives
- Borda count
D - non-dictorship

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11
Q

DWL equation

A

DWL = 1/2 * t^2/p * px * esed/es + ed

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12
Q

Optimal commodity tax and assumptions

A

min sum DWL s.t. sumtx > G:

  • t/pi / t/pj = ej/ei
  • Frank Ramsay: tax in proportion to G but goods with higher elasticity tax more
  • optimal is regressive tax

Assumptions: no lump sum, linear demand, cross-price elasticities = 0, constant MC

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13
Q

Cost benefit analysis

A

NPV = sum B-C/(1+r)^t

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14
Q

Coase Theorem

A

Irrespective of the allocation of property rights, frictionless bargaining produces the efficient of outcome in presence of externalities

  • different distributional consequences
  • frictions: legal, time
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15
Q

Tax vs quantity

A

Weitzman 1974:
- minimise DWL from error
MC> MB set quantity
MC < MB set tax

  • Price: double dividend from revenue, easier to change p than q
  • Tax: destination-based tax - displace consumption/investment. Tax product - mobility
  • how decide on the marginal external effect: IEA letter - model with lower emissions - too fossil fuel friendly
  • risk of carbon leakage: EU free allowances to safeguard industries at risk of carbon leakage

Quantity

  • regulation so not unanimous vote in council
  • price fluctuate - less incentive for RandD

1) Efficiency (if uncertainty) 2) Distributive 3) Political-Economical (enforcement - costly, EU)

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16
Q

Prisoner’s dilemma definition

A

Individual utility maximisation leads to a Pareto inferior outcome
- e.g. 19709 tobacco agreement - inc profits by $91m

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17
Q

Nash equilibrium defintion

A

a strategy profile such that each player’s strategy is a best response to the strategies of other players

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18
Q

Battle of the sexes

A

Coorindation game, need to coordinate to get highest payoff

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19
Q

Subgame perfect equilibrium

A

A nash equilibrium which induces a Nash equilibrium in each subgame

  • assume know each other’s payoffs
  • show using tree diagram (extensive form)
  • SPE: (L: l after L, r after R) so SPE is (L,l)
  • eliminates NE that rely on non credible threats/promises
  • collusion is not SPE in a finite game
  • small firms don’t have capacity to flood the market - not credible - damage them more than deviator.
  • large firm: predatory price - suffer larger losses but can do in selective markets
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20
Q

Trigger strategy

A

Play X as long as opponent doesn’t play y, in which case play Z. Grim: play Z forever.

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21
Q

Folk Theorem

A

Any feasible payoff pair which gives each player at least her minimax payoff can be supported in an equilibrium tof an infinitely repeated game if players are sufficiently patient.

Minimax: lowest payoff when playing best response

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22
Q

Finite repeated

A

The unique SPE is to play the stage game NE in every period.

  • final subgame is like one-shot
  • T-1: no credible threat of punishment to induce a player to play anything other than the Nash equilibrium
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23
Q

Why don’t always ban mergers

A
  • economies of scale (natural monopoly) - average cost is declining
  • high profits fund RandD
  • incentive to innovate
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24
Q

Factors affecting likelihood of collusion

A
  • n (mergers) - 77% cartels <7 participants
  • frequency of sales / transparency / algorithms / Albeak et al 97: Danish 93
  • TIMELINESS OF PUNISHMENT
  • Meeting competition clauses - JL
  • Multimarket contact: Bernheim & Whinston (1990)
    • Evans & Kessides (1994)
  • Common ownership: Azar et al 2018 - Jp, Citi 3-7%
    • exchange info, incentive to cheat
  • leniency programs
  • cost asymmetries (focal point: Scherer 1980)
  • Size effect: small firms more impatient & capacity constrained so can’t flood market
  • Demand stability - Green & Porter
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25
Q

Detecting collusion

A
  • high profits
  • Price parralism - independent, rational behaviour
    • algorithms help? Tacit collusion not covered by competition law. Algorithms: achieve collusion w/o any agreement or human interaction
  • ideally estimate demand and cost functions (above Nash levels)
  • leniency programs: Virgin and BA over fuel surcharges - Virgin immune if first to report - BA fine of £270m
  • ‘prima facie’ - price swapping
  • observing price war is not at odds with collusion (Green and Porter) - intermittent price wars
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26
Q

Penalties for collusion

A
  • Fines up to 10% of turnover in UK / EU
  • Prison sentences: chairman of Sotheby’s
  • Leniency for whistleblowers - US payment, EU protection
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27
Q

Merger: cost vs efficiency

A

Williamson 1968 graph
- Change in surplus = D - B
= square - triangle

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28
Q

UPP test

A

A increases price if merger with B means that:
- B’s (p-c) Dab > fall in MCa

  • diversion ratio: measure of substitutability. fraction sales lost by a that goes to b.
  • assumes no rival response, no synergies
  • firms have incentives to exaggerate synergies
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29
Q

Allow a merger

A

Bertrand: UPP
- good for industries with relatively flat MC

Cournot: ambiguous as downward sloping BR curves. Only proposed if synergies.
- good approx for industries with relatively high MC

Unilateral (shift non-cooperative equilibrium) vs coordinated affects (collusion more likely)

Vertical: double marginalisation - comp not increased when goods are compliments

Unless remedies can be found - e.g. Nestle - perrier had to loose some sources - dominance of mineral water in France

Steps: 1) see if inc market power - define market and assess 2) market power = inc price - efficiencies? 3) collusion?

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30
Q

Estimating MC

A 
Assume linear demand: 
- q = a - bp + gp
- differentiate profit w.r.t p: 
= a + bc - 2bp +  gp 
= a - bp + gp + (p-c) b = 0 
- demand + (price - mc)x slope of demand = 0
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31
Q

Relevant market

A

Minimal set of products over which a hypothetical monopoly would find it profitable to raise its price

  • SSNIP test: check if cross-price elasticity is > 1 then not profitable so add until < 1
  • e.g. if price increase provoke significant number of consumers to switch to another product - surveys.
  • Nestle / Perrier - French mineral water - wouldn’t lead to shift to soft drinks so profitable
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32
Q

Predatory pricing

A
  • set prices to sacrifice profits in ST to eliminate competition and get higher profits in the LR
  • relies on info asymmetry
  • less rational than merging but banned
  • large form, large loss, target markets
  • reputational impact
  • small firm could re-enter but this ignores the sunk-cost of entry and low recovery rate of fixed costs of exiting
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33
Q

Public good issue

A

Free-riding: incentive incompatible via non-excludability

  • whoever has highest MB pays and others benefit.
  • under provision
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34
Q

Public good provision

A

Samuelson condition: public goods not rival so enjoyed by many simultaneously. Sum MB = aggregate demand. MC = supply under competitive market
- voluntary Q < Q* since investment by others dec their MPB so dec their investment

Lump-sum: A pays relatively more in terms of MB

Lindhal pricing: consume up to MB = price = t

  • incentive to understate
  • can consume xb due to non excludability

Pivotal: impractical to implement - equity and administration costs
- if f(x) then not pareto efficient

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35
Q

Greenhouse gases

A
  • Tax vs quantity: assume steep MC so set quantity
  • Tech innovation: improve efficiency, reduce demands, alternatives
  • International competitiveness: country would effectively export its emissions-> trade deficit -> tariffs could be used to partially address this. Initial allocation with cap-and-trade can incentivise countries to join.
  • compliance costs, implementation, monitoring
  • Obtaining monetary values for B and C (uncertainty)
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36
Q

Pareto criterion and its disadvantages

Pareto efficient defintion

A

A superior if no i finds A worse than B and at least 1 i finds A better
- fails to deliver complete ordering. Can’t compare pareto and even some inferior to efficient. No allocative considerations.

PE: no other feasible outcome Pareto superior to it

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37
Q

Assumptions for social preference ordering

A

continuity, completeness, transitivity, reflexive and non-satisation

38
Q

Issues with Walrasian in reality

A

lack of rationality, not unlimited supply, not awareness of all prices in all locations

39
Q

Expected utility theorem assumptions

A

Complete, transitive, reflexive, continuity, independence

40
Q

Certainty equivalent definition

A

The amount of £ that gives you the same utility as the expected utility of the lottery
- show on graph u / y

41
Q

Absolute risk aversion

A

A(y) = - u’‘(y) / u’(y)
- allows comparison of attitudes to lotteries whose outcomes are absolute gains or losses from current wealth
- negative so risk aversion positive
- CARA: if you reaction to losing $10 is the same whether
you have $100 or $10,000

42
Q

Relative risk aversion

A

yA(y)

  • evaluate lotteries whose outcomes are relative gains or losses from current wealth.
  • CRRA: same reaction to losing 1% of wealth, no matter the wealth level
43
Q

Approximate risk premium and relative risk premium

A

r(y) = 1/2 A(y) * var

r(y)/y = 1/2 R(y) * var/y^2

44
Q

Log preferences: risk aversion?

A

CRRA -> DARA

45
Q

First order / second order stochastic dominant

A

Restricted to lotteries with same outcome.

  • 1st: CDF lies below then preferred. Unambigiously higher returns
  • 2nd: A preferred if B is mean-preserving spread of A. CDF lies crosses from below just once. Less risky (same mean outcome)
46
Q

Risk sharing

A

Risk premium falls fast than the expected value –> certainty equivalent falls

47
Q

Risk pooling

A

Opposite of mean preserving spread.

  • probability of middle value goes from 0 to 1/2.
  • not the case if perfectly positively correlated.
48
Q

Rothschild-Stiglitz diagram

A

State-contigent state:
- Slope: - 1-p/p u’(y1)/u’(y2)
-> p is probability of y2
-

49
Q

Fair insurance formula

Actuarially fairness explanation

A

Premium = probability of loss x compensation

Expected gain or loss for insurer is zero. Not impact their expected income.

50
Q

Why L-type must be on its zero-profit line but not full insuance

A

If full then H choose L package and firm makes a loss

If people line then profitable deviation then attract H and loss making. Its the best breakeven point that doesn’t attract H types.

51
Q

Signalling: why IC L is steeper

A

Cost of education is the disutility of education. Higher cost for L types.

52
Q

How pooling determined

Best separating

How worst signalling separating equilibrium is determined

A

Beyond e’ no incentive for L to pool - H signal by getting e to right of wage schedule but lower IC

Send distinguishing signal at lowest cost

e’’ is the highest level of education that the H types would be willing to undertake in order to differentiate themselves from low productivity workers.

53
Q

Why pareto efficiency at tangency points

A

Then set of points that A prefers to point X do not intersect with set that B prefers

54
Q

Agency cost equation

A

expected wage - certainty equivalent wage

  • CE wage: w in PC for high effort (observable case)
55
Q

What makes signalling credible?

A

Too expensive for L-types to copy

56
Q

Why some want to signal?

A

H types would like to signal and get wH rather than average productivity if cost is signal is less than wage difference

57
Q

Contracts when observable and not observable

A

Observable: (e,w)
Unobservale: (w,w) contigent on output

58
Q

How implement low effort

A

Offer a fixed wage that just satisfies then PC

59
Q

Why agency cost exists

A

The variable wage that assures the agent of reservation utility is greater than the fixed wage that does the same

60
Q

Bertrand: reasons why p not equal MC

A
  • capacity contraints
  • different MC
  • collusion in repeated interactions
61
Q

Why in Cournot, firm with lower MC has more profit?

A

1) Production cost fallen for any level of output (direct)

2) More aggressive = push out reaction function. In equilibrium: firm 2 produces less and firm 1 produces more

62
Q

Tragedy of the commons

A

Natural common resources are over-used/

  • Non-Excludable and partially rival
  • low-level use doesn’t negatively affect others but at higher levels have congestion
  • Non-Excludability: technological (monitoring) / legal problem (who owns)
63
Q

Lagrangian formula

A

L = utility - Lamda (spending - income)

aka income is positive

64
Q

Pigovian tax

A

The marginal externality (cost) at the optimal solution

65
Q

Iterated deletion of strictly dominated strategies

A

1st: any strategies that are dominated are deleted as no rational player would ever play
- now smaller game so some that weren’t dominated before now might be
- common knowledge of rationality is assumed

66
Q

When signalling may not be socially wasteful

A

1) H had an outside option > average productivity. Signalling overcome this adverse selection problem
2) signalling led to appropriate task assignment

67
Q

How show risk averse:

A
  • u’‘(y) < 0 (concave)

- take lower mean for less spread distribution

68
Q

What CRRA and DARA mean

A

CRRA: invested half of wealth so will invest have again
DARA: more wealth, take more risk, buy more insurance

69
Q

Why merger can be seen as collusion

A

Both internalise each other’s profits

70
Q

Problem with SSNIP

A

How define significant: 1%, 5%

  • non-transitory: going up for forever
  • usually 5% for 12 months
71
Q

When are social preference orderings consistent

A

Reflexive, transitive, complete

72
Q

Explain free-rider problem with public goods

A

Can’t get those who use to pay for it

  • Underprovision
  • Efficient production is samuelson
  • Financed through taxes but cause welfare losses
73
Q

What is a mixed strategy

A

allows randomisation, specifying a probability with which each pure strategy is selected
- allows an equilibrium when no pure NE exists

74
Q

Vertical and horizontal differentiation

A

Vertical Differentiation:
- Goods differentiated in quality, such that if both were the
same price, all consumers would buy the higher quality good and not the other

Horizontal differentiation:
Goods are differentiated in dimensions other than quantity
such that consumers differ in the ranking of the goods, even at the same price

75
Q

Policies to reduce collusion

A
  • reduce price transparency
  • ban mergers, especially if involve rogue competitors
  • whisteblowing / leniency
  • common ownership
76
Q

How lindahl pricing works

A
  • announcement of hypothetical prices, agents state demand, to gain info on quantity / cost desired individually and collectively.
  • incentive to understate demand
77
Q

Arguments against trade

A 
Short-term unemployment before retrain
Exploitation
Infant industry 
Extreme dependancy (political instability / natural disaster) 
Inability to satisfy world demand
78
Q

Problem with funding public good

A

Impossible to get a mechanism that is pareto efficient, no one paying above their valuations, strategy proof and enough money raised to cover cost

79
Q

Negative Externality problem

A

Bilateral externality problem: failure to internalise cost imposed on consumer

  • Solution: tax, quota, bargaining
  • need good legal rights, ability to agree division of gains, perfect info, perfectly transferable property rights
  • create missing markets for deplorable externalities
80
Q

Examples of cap and trade schemes

A
  • US sulphur dioxide trading scheme: 43% reduction by 2007 from 1990 levels
  • EU ETS 11,000 greenhouse gas pullers from 31 countries since 2005: 40% allowances auction. Others free to safeguard international competitiveness of industrial sectors at risk of carbon leakage.
81
Q

Risk premium

A

expected value (wealth + net return) - certainty equivalent

82
Q

Why Lindahl pricing in pareto efficient?

why not practical?

A
  • each consumer consumes where MB = p, this is because consumer expects to be excluded from consuming units she’s not purchased.
  • requires consumers to believe they’ll be excluded and there’s no reason for consumers to take their price as given
83
Q

Why social surplus o when N= Ne

A

Enter until until the individual net value of using the road is zero
- it is optimal to restrict N so that the benefit to the marginal driver is equal to the marginal social cost

84
Q

What are rose competitors

A

Small firms that value current market share highly (maybe no future): discount factor near 0

85
Q

Private provision of a public good

A
  • doesn’t yield efficient quantity when the good is not excludable since only consumer with highest MU curve will purchase and others will free-ride
  • with excludability, possibility of personalised prices
  • Club good: charge P > p then A won’t pay, Charge p = MU then no DWL – don’t have full info for this perfect price discrimination
86
Q

Screening (insurance) timing, determine L, how serve both

A

1) nature selects p, privately observed
2) firms simultaneously announce set of offered contracts
3) consumers select preferred contract

L: utility same for H, fair insurance for L

Screening - first best or separating - self-select

87
Q

Salat Switzer Reynolds

A

Cournot merger

  • insiders internalise negative pecuniary externality and dec their output
  • outsiders inc output which moderates the price increase
  • lower q rom insiders not compensated by inc price in industry
88
Q

Signalling timing

A

1) nature selects 0
2) Workers choose e
3) Firms observe e and simultaneously offer wage contracts - Bertrand
4) Workers decide, if any to accept

89
Q

First fundamental theorem of welfare economics

A

Competitive equilibrium supports the pareto efficient outcome
- any frictions goes against this

90
Q

b in moral hazard w = a + b(profit)

A

Incentivises high effort by linking the wage to profit, a noisy signal of effort which exposes the agent to risk

91
Q

Principal-agent with risk neutral

A
  • Set b = 1
  • ‘sell project’ to agent for price alpha =E(profit / e) - g(e) - u i.e. binding PC
  • agent’s objective is to now maximise social surplus
92
Q

Assumptions of screening

A
  • competitive risk neutral insurers, free entry and exit, no administrative or legal costs in providing insurance therefore zero profits in equilibrium

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