Microeconomics Flashcards
Competitive equilibrium definition and assumptions
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
Walrus’ law
What does it imply
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.
Assumptions of production economy (competitive equilibrium)
no increasing returns
free disposal
irreversibility of production
wages & prices are competitive
Trade model
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)
Stopler-Samulseon
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
Equity in efficiency
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
Second theorem of welfare economics
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)
Social welfare functions
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)
Define strategyproofness
no agent can report different preferences and be better off under the outcome of the social welfare function
Arrow’s impossibility theorem
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
DWL equation
DWL = 1/2 * t^2/p * px * esed/es + ed
Optimal commodity tax and assumptions
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
Cost benefit analysis
NPV = sum B-C/(1+r)^t
Coase Theorem
Irrespective of the allocation of property rights, frictionless bargaining produces the efficient of outcome in presence of externalities
- different distributional consequences
- frictions: legal, time
Tax vs quantity
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)
Prisoner’s dilemma definition
Individual utility maximisation leads to a Pareto inferior outcome
- e.g. 19709 tobacco agreement - inc profits by $91m
Nash equilibrium defintion
a strategy profile such that each player’s strategy is a best response to the strategies of other players
Battle of the sexes
Coorindation game, need to coordinate to get highest payoff
Subgame perfect equilibrium
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
Trigger strategy
Play X as long as opponent doesn’t play y, in which case play Z. Grim: play Z forever.
Folk Theorem
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
Finite repeated
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
Why don’t always ban mergers
- economies of scale (natural monopoly) - average cost is declining
- high profits fund RandD
- incentive to innovate
Factors affecting likelihood of collusion
- 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
Detecting collusion
- 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
Penalties for collusion
- Fines up to 10% of turnover in UK / EU
- Prison sentences: chairman of Sotheby’s
- Leniency for whistleblowers - US payment, EU protection
Merger: cost vs efficiency
Williamson 1968 graph
- Change in surplus = D - B
= square - triangle
UPP test
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
Allow a merger
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?
Estimating MC
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
Relevant market
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
Predatory pricing
- 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
Public good issue
Free-riding: incentive incompatible via non-excludability
- whoever has highest MB pays and others benefit.
- under provision
Public good provision
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
Greenhouse gases
- 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)
Pareto criterion and its disadvantages
Pareto efficient defintion
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
Assumptions for social preference ordering
continuity, completeness, transitivity, reflexive and non-satisation
Issues with Walrasian in reality
lack of rationality, not unlimited supply, not awareness of all prices in all locations
Expected utility theorem assumptions
Complete, transitive, reflexive, continuity, independence
Certainty equivalent definition
The amount of £ that gives you the same utility as the expected utility of the lottery
- show on graph u / y
Absolute risk aversion
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
Relative risk aversion
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
Approximate risk premium and relative risk premium
r(y) = 1/2 A(y) * var
r(y)/y = 1/2 R(y) * var/y^2
Log preferences: risk aversion?
CRRA -> DARA
First order / second order stochastic dominant
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)
Risk sharing
Risk premium falls fast than the expected value –> certainty equivalent falls
Risk pooling
Opposite of mean preserving spread.
- probability of middle value goes from 0 to 1/2.
- not the case if perfectly positively correlated.
Rothschild-Stiglitz diagram
State-contigent state:
- Slope: - 1-p/p u’(y1)/u’(y2)
-> p is probability of y2
-
Fair insurance formula
Actuarially fairness explanation
Premium = probability of loss x compensation
Expected gain or loss for insurer is zero. Not impact their expected income.
Why L-type must be on its zero-profit line but not full insuance
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.
Signalling: why IC L is steeper
Cost of education is the disutility of education. Higher cost for L types.
How pooling determined
Best separating
How worst signalling separating equilibrium is determined
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.
Why pareto efficiency at tangency points
Then set of points that A prefers to point X do not intersect with set that B prefers
Agency cost equation
expected wage - certainty equivalent wage
- CE wage: w in PC for high effort (observable case)
What makes signalling credible?
Too expensive for L-types to copy
Why some want to signal?
H types would like to signal and get wH rather than average productivity if cost is signal is less than wage difference
Contracts when observable and not observable
Observable: (e,w)
Unobservale: (w,w) contigent on output
How implement low effort
Offer a fixed wage that just satisfies then PC
Why agency cost exists
The variable wage that assures the agent of reservation utility is greater than the fixed wage that does the same
Bertrand: reasons why p not equal MC
- capacity contraints
- different MC
- collusion in repeated interactions
Why in Cournot, firm with lower MC has more profit?
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
Tragedy of the commons
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)
Lagrangian formula
L = utility - Lamda (spending - income)
aka income is positive
Pigovian tax
The marginal externality (cost) at the optimal solution
Iterated deletion of strictly dominated strategies
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
When signalling may not be socially wasteful
1) H had an outside option > average productivity. Signalling overcome this adverse selection problem
2) signalling led to appropriate task assignment
How show risk averse:
- u’‘(y) < 0 (concave)
- take lower mean for less spread distribution
What CRRA and DARA mean
CRRA: invested half of wealth so will invest have again
DARA: more wealth, take more risk, buy more insurance
Why merger can be seen as collusion
Both internalise each other’s profits
Problem with SSNIP
How define significant: 1%, 5%
- non-transitory: going up for forever
- usually 5% for 12 months
When are social preference orderings consistent
Reflexive, transitive, complete
Explain free-rider problem with public goods
Can’t get those who use to pay for it
- Underprovision
- Efficient production is samuelson
- Financed through taxes but cause welfare losses
What is a mixed strategy
allows randomisation, specifying a probability with which each pure strategy is selected
- allows an equilibrium when no pure NE exists
Vertical and horizontal differentiation
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
Policies to reduce collusion
- reduce price transparency
- ban mergers, especially if involve rogue competitors
- whisteblowing / leniency
- common ownership
How lindahl pricing works
- announcement of hypothetical prices, agents state demand, to gain info on quantity / cost desired individually and collectively.
- incentive to understate demand
Arguments against trade
Short-term unemployment before retrain Exploitation Infant industry Extreme dependancy (political instability / natural disaster) Inability to satisfy world demand
Problem with funding public good
Impossible to get a mechanism that is pareto efficient, no one paying above their valuations, strategy proof and enough money raised to cover cost
Negative Externality problem
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
Examples of cap and trade schemes
- 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.
Risk premium
expected value (wealth + net return) - certainty equivalent
Why Lindahl pricing in pareto efficient?
why not practical?
- 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
Why social surplus o when N= Ne
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
What are rose competitors
Small firms that value current market share highly (maybe no future): discount factor near 0
Private provision of a public good
- 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
Screening (insurance) timing, determine L, how serve both
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
Salat Switzer Reynolds
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
Signalling timing
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
First fundamental theorem of welfare economics
Competitive equilibrium supports the pareto efficient outcome
- any frictions goes against this
b in moral hazard w = a + b(profit)
Incentivises high effort by linking the wage to profit, a noisy signal of effort which exposes the agent to risk
Principal-agent with risk neutral
- 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
Assumptions of screening
- competitive risk neutral insurers, free entry and exit, no administrative or legal costs in providing insurance therefore zero profits in equilibrium
