Micro II exam

How to find quantity of a public good (G)when there are more people benefiting from it

(#of agents like A)|MRS_A|+(#of agents like B)|MRS_B|=MC(G)

The Laffer Curve, DWL from tax

- A higher tax rate, t, has two effects on revenue. 1) The revenue per unit increases, which has a positive effect on total revenue and 2) The number of units traded falls, which has a negative effect. Elasticities: The tax revenue decreases when the curves become more elastic, as then the tax reduces the equilibrium quantity more strongly. The DWL also increases in the elasticities of the two curves. The change in behavior is more pronounced if the elasticities are higher, leading to a greater distortion and greater welfare loss. Differentiate and find the point that maximizes tax revenue. - A trade in which the marginal benefit of consumption is ≥ than the marginal cost of production, increases market surplus. - The tax raises marginal cost (or lowers marginal benefit if levied on consumers) thus producers produce a lower quantity and consumers demand a lower quantity. - This means that the tax prevents some trades that, without the tax, would have happened because MB ≥ MC and thus would have added surplus. - When the tax increases, the difference between MB and MC in the trades it 'prevents' is larger (remember that each point on the demand curve represents the marginal benefit of the marginal consumer). This leads to a higher fall in surplus!

Games with many players

- A strategy set of possible strategies for each player, S1, S2, ..., SN - Utility functions that indicate each player's utility as a function of the strategies selected - A best response function for player i indicates an optimal strategy for player i as a function of other players' strategies -A Nash equilibrium is a set of strategies for all players which are best responses to each other. It follows that in a Nash equilibrium, each player has maximized utility given what everyone else does.

What types of price discrimination gives the monopolist the highest profits?

1) 1st degree gives the highest profits, since the monopolist here knows the exact willingnesses to pay for the consumers, which he charges. TS=PS and CS=0. 2) 3rd degree gives higher profits than 2nd degree. With 3rd degree, the monopolist can tell the consumer types apart and charge different prices. With 2nd degree, he cannot tell them apart, why he is charged an information cost to make sure the one group that is most willing to pay does not buy the other group's cheaper product, an IC constraint. This information rent benefits consumers.

How to overcome DWL from monopolies

1) force the monopolist to increase production to the optimal level by law, or by letting the government directly take over production 2) introducing price controls (price ceiling) 3) introduce subsidy to get the monopolist to raise production to the efficient level The solutions to monopoly obviously require the government to have a lot of information about preferences / technology etc.

Calculating DWL from a tax (math)

1/2*t*(x*-x^t)

Nash equilibrium

A Nash equilibrium is a set of strategies for the two players which are best responses to each other "In a Nash equilibrium, I cannot make myself better off by changing my behavior" Coordination game: when there are more than one equilibria

principal-agent problem

A PA-problem makes the firm best off under the condition that the agent gets their outside option-utility (Individual Rationality Constraint) and that their utility from abiding with the contract is higher than the utility of not doing so (Incentive Compatibility Constraint) = Pareto optimal OBS: Moral Hazards; that the agent has incentives to misbehave after taking the contract. Could be solved by franchising or extreme performance pay, but NOT profit sharing Always look for edge solutions!! It might be best for the Principal not to offer the job!

Oligopoly

A market structure in which a few large firms dominate a market. Compared to perfect competition, we move away from the assumption of price-taking; the firms know that their production decisions will affect the price.

Elasticity

A measure of the relative change in demand for a given relative change in price. e(x*)=D'(p*)*(p*)/D(p*)

Network effects (monopoly)

A reason to have a monopoly is the presence of network effects: firm's consumers benefit from having more fellow consumers. Example: - Software platforms: more users => better for developers => more developers => better for users => more users ....

Production quotas when we have externalities (cap and trade) - and problems

A simple solution to externalities: Prohibit firms to produce more than socially optimal amount problematic in practice: policymakers will have to know the intersection between SMC and the demand curve, which requires a detailed knowledge of firms, technology etc. Another problem is how to determine which firms should be permitted to produce - this can be solved by letting firms trade their quotas (quotas for pollution or permits for the socially optimal amount of production)! A cap and trade system implements the socially optimal production level because the equilibrium price of quotas (per unit of good) becomes equal to the marginal external cost With permits, policymakers need to know the socially optimal level of CO2 emission - with pigou taxes, they had to know the marginal external cost. In general, quotas are better because they price the pollution (direct effect) instead of changing the price of steel (indirect effect on pollution)

Strictly / weakly dominating strategies

A strategy for player 1, s1, is weakly dominated by another strategy, s1', if s1' makes player 1 weakly better off regardless what player 2 does. Utility with s1' is always higher than or equal to utility of s1. s1 is strictly dominated by s1', if s1' makes player 1 strictly better off regardless of what player 2 does: utility with s1' is always higher than utility with s1. A strategy that is strictly dominated will never be played in Nash equilibrium, as it can never be a best response. A strictly dominating strategy will always be played in equilibrium: it will always be the only best response.

Credit rationing / moral hazards on the Loaning Market

An entrepreneur wants to borrow money for a project. He can choose a risky project with a high sales potential, or a less risky project with a lower sale potential. The bank would prefer the lower risk. If the entrepreneur has a risk of bankrupcy, the bank will demand a high interest rate; the high interest rate might make the entrepreneur make an even riskier choice because this can give him a higher potential sale (though with higher risks). It will be optimal for the bank not to lend the money. => Moral hazards on the Loaning Market can mean that high interest rates will cause a very risky behavior, why it can be optimal for banks to decline giving loans (credit rationing)

Why do monopolies exist?

Because of barriers to entry that prevent other firms from entering the market. High average costs with low production, why only one or few firms can be in the market with large production at the same time.

Cardinal v. Ordinal

Cardinal: how many (absolute utility) Ordinal: what order (comparative utility)

Insurance companies choosing contracts (cautious or careless contract)

Cautious contract: lowers the expected costs because the risk is lower, but demands a lower price to be accepted (same as without moral hazards) Demands deductives (selvrisiko) which lowers the agents' willingnesses to pay, and demands a lower price for the agent to accept.

2nd degree price discrimination

Charging different prices based on the quantity purchased Assumption: the monopolist can't tell the difference between different types of costumers - so he can't control what packages the different consumers buy. It is a PA-problem. Each consumer's CS(x) is the maximum amount they are willing to pay for receiving x units, and not having to pay a per-unit price. We can write up IRs and ICs for consumer A and B: IRs: they will rather buy their packages than not buy anything ICs: they will buy the package intended for them (and not the one intended for the other consumer group) Typically, each consumer has a binding constraint. We will typically have one binding IR and one binding IC, or two binding IRs. We can test this - use qualified guesses. More often than not, the consumer with the highest willingness to pay will have a binding IC. We need to check for corner solutions!

Coase Theorem

Coase theorem pt. 1: Coase suggested that: If all property rights are assigned, the end result will be efficient, no matter how the property rights are assigned. It is the proposition that: if private parties can bargain without cost over the allocation of resources, they can solve the problem of externalities on their own The modified Edgeworth box with externalities illustrates the Coase Theorem; if we assign property rights over the externality and allow trading to take place, we are back to the Walras equilibrium from Micro I. The first welfare theorem holds for this economy, so the equilibrium is efficient! Coase Theorem pt. 2: If the agents have quasi-linear preferences, the equilibrium quantity of the externality is independent of how the property rights are distributed. We end up with the same amount of smoke/music (whatever the externality) in equilibrium!! SO: Quasi-linear preferences => No income effects => Willingness to pay is independent of the level of income

First Welfare Theorem

Competitive equilibrium is Pareto-efficient

Monopoly - how to determine price/quantity

Cost minimization and profit maximization - MC=MR. This is because when a monopolist lowers price, he will have to lower the price for all other units he already supplies (only under monopoly!) The MR curve is equal to the demand curve, except with double the slope. (for linear demands)

Giffen Good

Demand increasing in its own price

Signalling

Education as signalling: education helps skilled people prove that they are skilled - works when education makes you productive, or if it doesn't have an effect on productivity.

contracts with efforts

Employments with salaries w and efforts e to get the job - the agents' utilities depend positively on their salary and negatively on their efforts to get the job

Walrasian equilibrium

Equilibrium occurring as if it was assisted by an "auctioneer", where quantities supplied and demanded eventually meet. Step one: maximize both people's utilities in terms of the two goods, under the condition of their income. Step 2: Calculate the price of the good that you don't know the price of Step 3: find the amounts in equilibrium. Some times you need to calculate utilities at these amounts.

Single-peaked preferences

Every agent has a favourite option, and just wants to get as close to this option as possible

Social choice functions

Every agent has a preference relation over A (the amount of possible states). A SCF aggregates the individual preferences to a total society-preference It is a rule or a system that determines how we make decisions in a society - it tells us how society ranges different states. Options to determine SCF: democracy/dictatorship

Symmetrical missing information

Everyone knows that half of all cars are good and half of all cars are bad; decisions are made due to expectations. The buyer will offer the same price regardless of the quality of the car. The sellers do not know what quality their car has - all cars are still traded, here at the same price (the average price) Sellers with bad cars are very well off, buyers of a good car are very well off.

Risk averse agent in PA-problems

Franchising and performance pay won't be efficient - the agent will accept a risk premium

Tax revenue

Government income due to taxation. Calculated: t*q

How to aggregate demand curves

Horizontal addition with private goods Vertical addition with public goods

Perfectly elastic supply (demand)

Horizontal curve. Supply: At a given price, suppliers will supply an infinite amount of goods (Demand: At a given price, buyers will buy an infinite amount, at higher prices they will by nothing at all)

Transitive Preferences

If a>b and b>c, then a>c

Second Welfare Theorem

If all consumers have continuous, monotone and strictly convex preferences, and there is a positive supply of all goods, a Pareto-optimal allocation will also be a Walrasian equilibrium.

Arrow's Impossibility Theorem: 2) Pareto Unanimity (PU)

If every individual prefers a certain option to another, then so must the resulting societal preference order in the SCF.

One curve perfectly inelastic vs. one curve perfectly elastic:

If one curve is perfectly elastic, it determines the equilibrium price and the other curve determines the quantity. If one curve is perfectly inelastic, it determines the equilibrium quantity whereas the other curve will determine the price.

Information costs and rents

In the case of asymmetric information there might be information costs to one party. For instance the principal might use signaling, which creates costs for the agents, which has to be compensated. In cases where the principal has to increase the contract of one agent above its reservation utility in order to prevent that agent of switching to another contract, that agent earns informations rents.

Price-setting in the long/short run

In the short run fixed costs are sunk, zero production can be optimal if x* gives negative profits. In the long run (shutting down avoids fixed costs) closing can be optimal if x* yields negative profits

Risk averse agent, risk neutral principal

In this case it is efficient that the firm takes on all risk, because this makes the agent's willingness to pay higher!

MC for suppliers can easily be found by...

Inverse supply function, or derivative of total cost function c(x)

Franchising - when is it optimal?

It can be optimal no matter if the agent is risk neutral or risk averse, in a case where the principal can't observe the effort of the agent after the contract has been signed. However, if there is a random component (a risk of some event happening that will lower profits), the risk-averse agent will have a lower willingness to pay for the franchising contract - this will lower the principal's expected profits, why there is an information cost to the principal.

Individual Rationality Constraint

It has to be rational to take the job; better than outside option/utility reservation

Monopsony

Market with only one buyer. If we look at a city of 100 people where all are employed by the same firm, the labour market is a monopsony - the only "buyer" of labour is the one firm, why they choose the price of labour / the pay.

How to find social optimum with two firms and an externality

Maximixe total profits of the two firms - this will take the negative effect of the externality into consideration, and maximize total surplus

Pooling vs. seperating equillibrium

Med asymmetrisk info får vi pooling equilibrium, hvor den fælles pris p* afspejler et vejet gennemsnit af MC Det betyder, at høj-risiko-typer overforsikres, lav-risiko- typer underforsikres. Der opstår dødvægtstab sammenlignet med symm.info; igen: Asymm.info giver både inefficiens og fordelingsvirkninger. I et kompetitivt miljø vil resultatet, hvis selskab kan skelne mellem typer, blive separating equilibrium med forskellige vilkår: Hver type afkræves en pris svarende til typens MC. I denne kompetitive ligevægt får selskab nul i forventet profit; vi opnår desuden efficient "market outcome".

Monopolist produce on the elastic part of the demand curve (intuition)

Monopolists always produce on the elastic part of the demand curve (|e(x*)|≥1) - It is never optimal to increase production so much that you get to the inelastic region. Intuition: if demand is inelastic at a given price and quantity, then it is always optimal to raise the price a bit. If the demand curve is inelastic, an increase in price by 1% will drop quantity by less than 1%. The monopolist sets a price equal to the marginal cost times a term depending on the price elasticity of demand - follows a markup pricing rule. Idea: less elastic demand => more market power for the monopolist. p*=1/(1-(1/(|e(x*)|)))*MC(x*)

Moral Hazards of Insurance

Moral hazards causes deductives (selvrisiko) - if the principal wants the agent to be carefull, then the agent has to bear some of the loss Moral hazards causes an information cost for the firm - mathematically, a binding conditionality in the profit maximizing problem => lower profits

public goods

Non-rival and non-excludable.

Pigouvian tax definition - and when does it/not work?

Per-unit tax, to achieve the social optimal level. Pigou tax works because it raises the marginal cost for firms, which makes them internalize the marginal external cost. The pigouvian tax equals the marginal cost of the externality at the socially optimal level. Reaching the social optimum requires that policymakers know the marginal external costs at the socially optimal level Pigou's idea was to tax production/sales; if we can measure the amount of emitted pollution per firm, we can also tax pollution directly Problem: With permits, policymakers need to know the socially optimal level of CO2 emission - with pigou taxes, they had to know the marginal external cost. A Pigouvian tax is a "per unit"-tax - it only works when the production is directly linked to the externality. If the firm can change the level of the externality without affecting the production, the Pigouvian tax won't work. A Pigouvian tax on their production would thus lower the production and minimize the social optimal levels of production.

How to find best response in a Nash Equilibria

Player 1: for the left values, pick the highest number in each column. Player 2: for the right side values, pick the highest number in each row.

Static games

Players make their choices simultaneously (and only once): i.e rock paper scissors without repetition, but NOT chess.

Rational Preferences

Preferences are complete (exists a preference for all options) and transitive (an ordinal ranking of what options are preffered - if apples are better than pears, pears better than oranges, then apples are better than oranges)

The Bertrand model

Price competition between two firms under oligopoly. VERY different to Cournot. Perfectly elastic supply, therefore we get the perfect competition price and amount! Assumptions: - If the prices are different, all consumers buy from the firm with the lower price. - If the firms set the same price, they split the consumers evenly between them. - The produced quantity follows from the demand function. If the two firms have different marginal costs, the one with the lower marginal costs will get the entire market.

Cournot Oligopoly

Quantity competition under oligopoly. Perfectly inelastic supply (?) We can find NE - best responses to each other, given how much the other firm produces. (given quantities, not prices). The two firms share the market. The equilibrium is more efficient than monopoly, less efficient than FKK. As in the case of perfect competition and (most of the time) monopoly, we have analyzed this assuming firms who choose quantities, not prices.

Types of welfare functions

Rawls SWF: measures welfare of the poorest member Utilitarian/Bentham SWF: addition

Arrow's Impossibility Theorem: 1) Universal Domain (UD)

SCF shall be defined for all rational preferences over A (everyone has complete and transitive preferences)

1st degree price discrimination

Seller charges each buyer their maximum willingness to pay. Assumption: the monopolist has perfect information on all consumers' willingnesses to pay (unrealistic) TS=PS CS=0 It is efficient; we get the perfect competition-equilibrium, but the monopolist takes all the surplus. No DWL.

Assymetrical Information

Sellers know what type of car they have (good/bad), but the buyer will not know until they buy the car. Only the bad cars are traded - inefficiency. The lower the price, the higher is the probability of only the bad cars being traded.

Taxes under monopoly

Simple: MR(x)=MC(x)+t Higher costs. Under perfect competition, consumer prices increase between 0 and t when the tax is introduced; under monopoly, consumer price may increase by more than t.

What is in an anatomy table? How can we use it? What can we do with only the left side (no assumptions on behavior and equilibrium)?

Technology and preferences (left side): - Exogenous functions/variables/relations - Endogenous variables Behavior and equilibrium (right side): - Agents' decisions (maximization problems) -> Conditional behavior (the "*"-amounts) - Equilibrium conditions (endowments equals how much is used in equilibrium) When we only have the left side, we can: - Find the agent's utility - Find Pareto-stable allocations - Comparative statistics

The Modified Edgeworth Box with externalities

The Modified Edgeworth Box with externalities illustrates the Coase Theorem: if we assign property rights over the externality and allow trading to take place, we are back to the Walras equilibrium from Micro I. The first welfare theorem holds for this economy, so the equilibrium is efficient! Coase Theorem pt. two in this: If the agents have quasi-linear preferences, the equilibrium quantity of the externality is independent of how the property rights are distributed SO: Quasi-linear preferences => No income effects => Willingness to pay is independent of the level of income. The contract curve will be a horizontal line and the equillibrium amount of smoke is the same in all equilibria.

How is tax burden divided?

The burden of the tax falls more on the side of the market that is less elastic.

price discrimination

The business practice of selling the same good at different prices to different customers. Only under monopoly. 1st degree: monopolist has perfect information on marginal willingness to pay. Not the case under 2nd and 3rd degree.

Externalities create inefficiency in a Nash equilibrium - why?

The equilibrium does NOT coincide with the social optimum - the welfare theorems fail. Nash equilibria are generally inefficient because players' actions affect others' payoffs. Welfare theorems fail because there is no "market for externality"

Quasi-Linear Preferences

The marginal rate of substitution between good 1 and good 2 depends only on the current level of consumption of good 1. MRS is therefore equal for any given value of good 1.

Equivalent Variation (EV)

The maximum amount of money a consumer would be willing to lose in order to avoid dealing with a price increase (for taxes, this is equal to the DWL) The DWL for consumers is with quasilinear preferences: EV=(Delta)CS

free rider problem

The problem of a firm not producing a public good (even though they benefit from it) because they can benefit from the other firm's production without producing themselves.

Arrow's Impossibility Theorem: 4) Independence of irrelevant alternatives (IIA)

The social preference between x and y should depend only on the individual preferences between x and y. More generally, changes in individuals' rankings of irrelevant alternatives (ones outside a certain subset) should have no impact on the societal ranking of the subset. For example, if candidate x ranks socially before candidate y, then x should rank socially before y even if a third candidate z is removed from participation.

Arrow's Impossibility Theorem: 5) Non-dictatorship (ND)

The social welfare function should account for the wishes of multiple voters. It cannot simply mimic the preferences of a single voter.

Arrow's Impossibility Theorem: 3) Rationality Criteria (R)

The societal preferences in the social choice function shall be rational (complete and transitive)

Theory of Second Best

The theory is about how different market failures can happen simultaneously (ex. monopoly and pollution) If there are more failures present, the simple welfare results might not count. it might be better to "choose the lesser of two evils" monopolies (bad!) pollution (bad!)

Complete preferences

There exists a preference for all options - all pairs of options can be compared

Vickrey-Clarke-Groves Mechanism

VCG incitament to signal too high: if all signals are too high, and costs of the good are split equally! Introducing Clarke taxes: a pivotal tax on the agent that tips the decision from not producing to producing - he has to pay a Clarke tax corresponding to the other agents' loss of the decision pivoting. It is a Nash equilibrium that everyone speaks the truth! If they lie, they will pay the Clarke tax which will be higher than their utility. Assumption: quasi-linear preferences

Perfectly inelastic supply (demand)

Vertical curve. Supply: A given quantity is supplied no matter what the price is (Demand: A given quantity is demanded no matter the price)

The median selector theorem

We assume that all agents have single-peaked preferences where x is the ideal point for every agent. The agent is a median voter if their vote is the median of all votes. The theorem says that the median voter's vote is the optimal for society (a Condorcet winner) under a democracy SCF. The median voter's ideal point wins any pair-voting, and is optimal

Utility Possibility Set (UPS)

What combinations of benefits are possible for us to achieve in a two-person-economy. To find UPS, it is useful to first consider the Utility Possibility Frontier: The combinations of utility where A is made as well off as possible given B's utility. The solution to the problem from before can be seen as a function: If B is to have the utility u*, what is the highest utility A can get? UPF: the frontier! It is the amount of efficient states, just like the contract curve, just in a coordinate system instead of an Edgeworth Box. Social utility is maximized when both people's utilities are maximized simultaneously

In regard to trading, when will trading make both people better off?

When MRS^(A) is not equal to MRS^(B)! When MRS^(A)=MRS^B, no one will be better off without the other person being worse off.

crowding out when a firm increases production of a public good that another firm benefit from

When firm B increases contribution to the public good, A will decrease their contribution. Full crowding out only happens with quasi-linear preferences.

inferior good

a good that consumers demand less of when their incomes increase

normal good

a good that consumers demand more of when their incomes increase

Lerner Index

a measure of a firm's markup, or its level of market power. : -1/e(x*)

Public good

a shared good or service for which it would be impractical to make consumers pay individually and to exclude nonpayers

Condorcet Paradox

a situation in which a series of pair-wise majority votes over more than two options leads to a cycling of winners => when the society preferences are not transitive under democracy, why democracy can prove to be problematic, even though all agents have transitive preferences

Arrow's impossibility theorem

a theorem that demonstrates that a voting method that is guaranteed to always produce fair outcomes is a mathematical impossibility. He has set 5 conditions that a good SCF should always abide with - but they can mathematically never all be abided with at the same time. 1) Universal Domain (UD): SCF shall be defined for all rational preferences over A 2) Pareto Unanimity (PU): If every individual prefers a certain option to another, then so must the resulting societal preference order in the SCF. 3) Rationality Criteria (R): The societal preferences from the social choice function shall be rational, i.e. complete and transitive. 4) Independence of irrelevant alternatives (IIA): The social preference between x and y should depend only on the individual preferences between x and y. More generally, changes in individuals' rankings of irrelevant alternatives (ones outside a certain subset) should have no impact on the societal ranking of the subset. For example, if candidate x ranks socially before candidate y, then x should rank socially before y even if a third candidate z is removed from participation. 5) Non-dictatorship (ND): The social welfare function should account for the wishes of multiple voters. It cannot simply mimic the preferences of a single voter. If N≥2 and A has at least 3 different options, no SCF will abide with all 5 conditions. A SCF making one person a dictator, will abide with (UD), (PU), (R) and (IIA). (4 of the conditions)

best response function

an optimal strategy for player 1 as a function of player 2's strategy. First step towards equilibrium: Player 1 takes player 2's choice s2 as given and maximizes utility => solution is the best response (function of s2)

3rd degree price discrimination

charging different prices to different groups of consumers with varying elasticities Assumption: the monopolist can tell the difference between the types of consumers and sets different prices to them; but the monopolist doesn't know the marginal willingnesses to pay

DWL with taxes when we have quasi-linear preferences

competitive equilibrium maximizes total welfare (CS+PS). Taxes move us away from competitive equilibrium => always creates inefficiency when both have quasi-linear preferences! In the extreme scenario where either supply or demand is perfectly inelastic there is no dead weight loss. Intuition: The dead weight loss occurs because some gains of trade cease to exist and a high elasticity results in a more severe drop in traded quantity.

luxury good

good for which demand increases faster than income when income rises

Cournot profit of firm 1 given firm 2's produced quantity?

pi=p(x1+x2)*x1-C(x1) Maximize this with regard to x1.

Indifference curve for agents

profits on x-axis and utilities on y-axis. Indifferencecurves of utility are conveks. Profits are higher on the south-east, utilities are higher on the north-west. Isoprofitlines are linear/growing.

Agenda setting power

restrictions on the voting order to decide the social choice. The order means everything for what will be chosen

Tragedy of the Commons

situation in which people acting individually and in their own interest use up commonly available but limited resources, creating disaster for the entire community - indvidual decision-making leads to over-consumption!

Compensating Variation (CV)

the amount of money one would have to give a consumer to offset completely the harm from a price increase

mechanism design

the part of game theory concerned with designing the rules of a game so as to maximize the likelihood of players reaching a socially optimal outcome. The agents have to signal there preferences for a public good, and from all signals, the state decides how much to produce of the good and how much each agent has to pay.

Adverse Selection

the problem of incomplete information - of choosing alternatives without fully knowing the details of available options. Adverse selection can make markets break down. Example: PA-problem with highly productive vs. low productive agents. The market for highly productive agents can shut down because their high outside option / reservation salary can attract many less productive agents.

Incentive Compability Constraint

u(s,x)≥u(s,x') The agent needs incentives to abide with their contract. Their utility from abiding with the contract is higher than the utility of not doing so. There can be no other amount of working hours x' that the agent likes more than the amount in the contract, x.

pure strategies

we do not allow players to act randomly