Intermediate Microeconomics Midterm topics

What is the Pareto optimal allocation with an externality?

Pareto's efficiency here means maximizing the utility of the representative consumer. It is where the consumer consumes all the production c1 = y1, c2 = y2.

What is perfect information?

Platers move (make decision) sequentially and know the full history of play when it is their turn to move

In the centipede game, the backwards induction equilibrium is to:

Play "take" at every turn

Which voting methods satisfy the Pareto property?

Plurality and Borda

Which voting methods do not satisfy IIA?

Plurality, Borda, Sequantial pairwise voting w/ fixed agenda

examples of negative externalities

Production: Plants produce co2, noise Consumption: smoking, noise from neighbors

Examples of positive externalities

Productive: bees and orchard, free software Consumption: Telecom network, vaccination

What are the criteria for optimizing behavior?

The player needs to: - understand what other players will do - understand what others think that they will do

What is universality?

The preference aggregation rule F applies to all possible preference profiles

Numerical representation of majority rule

we replace the the ordering by a numerical score and the voting by a summation

What are violations of optimality axioms?

weighted majority voting and supermajority rules

When are mixed strategies useful?

when bluffing seems advantageous: penalty kicking, poker, serving in tennis

Is the Borda rule paretian?

yes

What is the indifference principle?

The principle of indifference states that in the absence of any relevant evidence, agents should distribute their credence (or 'degrees of belief') equally among all the possible outcomes under consideration.

What does agenda setting power mean?

Whoever gets to choose the order in which the rounds are organized decides the outcome of the vote

Does utilitarianism imply Pareto efficiency?

YES always

Are all Pareto improvements always Kaldor Hicks?

Yes

Is the plurality rule manipulable?

Yes

Does Walras totannement improve efficiency?

Yes but will keep a similar degree of fairness

Is the competitive equilibrium efficient without externality?

Yes, because MRS=MRT. Efficient allocation can be decentralized by the competitive equilibrium

Is the plurality rule complete and transitive?

Yes, but it yields ties

Does pairwise majority satisfy Arrow's theorem?

Yes. Pairwise majority does not generate cycles. The median of the voters' most-preferred alternatives will defeat any other alternative in a pairwise vote.

How do you check concavity of a utility function?

You take the second order derivative and check if its smaller than 0

What is a utility function?

a function that represents individuals preferences. Income - taxes +tax transfers

True or false: For any game, if we iteratively eliminate dominated strategies, we eventually end up on a unique strategy left for every player which gives us the equilibrium

(check idk)

Every finite game (i.e. each plater has a finite number of possible actions) admits a mixed strategy Nash equilibrium

- A mixed strategy Nash equilibrium always puts probability 0 on any action that is eliminated by IESDS. - Another way to understand mixed strategy equilibria is to interpret probabilities as the frequencies of different types of agents in a population. Mixed Nash equilibrium = heterogeneous optimal strategies

How to solve the commitment problem?

- A symmetric form of commitment is necessary - vertical integration (one firm decides for the other one) - Reputation and long term relationship

Assuming we are in a standard case (convex indifference curves), in a competitive equilibrium:

- Agents each maximize their utility subject to their budget constraint - Aggregate supply equals aggregate demand for each good - Walras law is satisfied - the price of each good is not uniquely determined: only the price ratio is

When do you apply game theory?

- Firms' strategic behavior (oligopolistic competition) - Bargaining - Auctions (eBay, spectrum auctions, google auctions) - Market design (matching markets)

What are properties of sequential move games?

- In every finite, perfect information game, there exists a backward induction (sequential rationality) solution - Backward induction always yields a Nash equilibrium of the associated normal form game - Some Nash equilibria of the normal form game may be inconsistent with backward induction

What are the solution concepts for a game?

- Iterative selection of strictly dominant strategies: gets rid of obviously dominates strategies, rarely yields to a unique equilibrium - Nash equilibrium: natural refinement, fewer but still many solutions

What are the possible limitations of a competitive equilibrium?

- There can be multiple equilibrium - There can be no equilibrium - Doesn't generally happen with convex indifference curves

Arrow's Impossibility Theorem

- Universal domain - Pareto property or unanimity - Independence of Irrelevant Alternatives - Dictatorship and Arrow's impossiblity theorem -Single-peaked preferences

Pareto efficiency with monetary transfers

- Willingness to pay - Pareto improving monetary transfers - Utilitarian solution to the social problem

In the aggregate welfare function (1 - µ)*U1 + µ*U2, the parameter µ:

- determines the eventual utility level of individual 2, assuming we enforce the allocation proposed by the social planner - denotes how much the social planner weights the welfare of individual 2 - denotes the Pareto weight of individual 2

What are limitations of implementing a quota to restore efficiency?

- how to know the correct amount for the quota? - the production technology is better known to the firms than to the governments - you need to prevent cheating by the firms to enforce it

Assuming convex preferences, the second welfare theorem (check all that apply):

- states that it is possible to obtain every Pareto efficient allocation as the outcome of a competitive equilibrium, provided the initial endowment is fixed accordingly - implies that, after adequate wealth transfers, it is possible to use competitive equilibrium to attain an allocation that is simultaneously efficient and fair - Pareto efficient allocations obtained through competitive equilibrium are definitely not necessarily fair.

Nash Equilibrium is a stability concept because:

-At a Nash equilibrium, no player has an interest to change strategy if every other player keeps the same strategy. -At a Nash equilibrium, it is impossible for two players to change their strategy simultaneously and reach an equilibrium that Pareto dominates the Nash equilibrium

What is the difference between Pareto efficient, Pareto frontier, Pareto improvement?

-Pareto improvements will keep enhancing value to an economy until it achieves a Pareto equilibrium, where no more Pareto improvements can be made. - Conversely, when an economy is at Pareto efficiency, any change to the allocation of resources will make at least one individual worse off. - the Pareto frontier shows all the Pareto efficient solutions--> it shows you all the points where the two indifference curves are tangent (hence, when MRS1=MRS2)

Strategy dominance

-the prisoner's dilemma - elimination of dominated strategies - the beauty contest

What are preference restrictions?

1) No monetary altruism: i does not care about t 2) Paying less is preferred 3) Compensation is possible 4) No wealth distortion

What is the equilibrium principle?

1. Firms maximize profits given prices 2. Consumers maximize utility given prices and income 3. Markets clear

What is needed for an efficient market equilibrium?

1. No externalities 2. Perfect competition 3. No transaction costs 4. Full information

What are the criteria for a competitive equilibrium?

1. rationality 2. markets clear (demand=supply)

Individual rationality

: A concept used to describe the behavior of an individual pursuing individual goals that maximize self-interest. --> when the individual chooses "more" rather than "less" and when he is consistent in his choices.

How to rank with Coombs system?

: several rounds of "reverse"-plurality voting are organized: citizens vote to exclude their least prefered candidate. At the end of each round, the candidate with the most votes is eliminated, and the remaining candid

In a game:

A Nash equilibrium in mixed strategy can exist where a Nash equilibrium in pure strategies does not exist

What is a Pareto improvement?

A change to the economy which leaves (1) everyone at least as well of and (2) someone strictly better off. Win-win

What are single-peaked preferences?

A group of agents is said to have single-peaked preferences over a set of possible outcomes if the outcomes can be ordered along a line such that: 1. Each agent has a "best outcome" in the set 2. For each agent, outcomes that are further from his or her best outcome are preferred less. - Are a way to escape Arrow's paradox. First, they guarantee that a Condorcet winner exists and further that the pairwise majority relation is transitive

What does dictatorship mean?

A social preference is a dictatorship if there is some individual i such that the social ranking is always exactly i regardless of the preferences of other individuals.

What is strict dominance?

A strictly dominated strategy is a strategy that ALWAYS delivers a worse outcome than an alternative strategy, regardless of what strategy the opponent chooses. - best reponse - unique best response

What is weak dominance?

A weakly dominated strategy is a strategy that delivers an equal or worse outcome than an alternative strategy. represented with > and equal sign

The market clearing conditions impose that:

Aggregate demand equals aggregate supply for every good

What does the first welfare theorem state?

All competitive equilibria are Pareto efficient.

What is a Kaldor-Hicks improvement?

Any change in the economy which increases the total value available to everyone in the economy. -If those that are made better off could in principle compensate those that are made worse off, so that a Pareto improving outcome could (though does not have to) be achieved

What is a pareto improvement on the Edgeworth box?

Any point inside the lens defined by the two indifference curves is a Pareto improvement.

What is backward induction reasoning?

Backward induction in game theory is an iterative process of reasoning backward in time, from the end of a problem or situation, to solve finite extensive form and sequential games, and infer a sequence of optimal actions.

Why does dictatorship satisfy unanimity (UN)?

Because if everyone prefers a to b then so does i

Why does dictatorship satisfy universal domain?

Because it always produces a well-defined ordering

Why is the market for pollution rights a better solution for externalities than taxation and quotas?

Because the government does not need to calculate the Pareto allocation to calculate the optimal quotas or taxes (COASE's theorem)

Why does dictatorship satisfy IIA?

Because the social ordering of any pair a,b only depends on i's ordering of a,b

How can we change the distribution of utilities?

By lump-sum redistribution

How do you obtain the Pareto frontier?

By maximizing aggregate welfare

What are the 3 types of utility functions?

Cobb-Douglas Quasi-linear Perfect substitutes

Restrictions on individual preferences that allow for individual rationality

Complete preferences Transitive preferences

What does the second welfare theorem state?

If all agents have convex preferences, then there will always be a set of prices and appropriate initial endowments (or incomes) such that each Pareto efficient allocation is a market equilibrium --> implies that there is no trade-off between efficiency and equity

What does µ represent?

Determines how much more or less the planner wants to favor one individual with respect to the other. It is the Pareto weight

Which Social Welfare Function satisfies simultaneously Universal Domain, Pareto Efficiency and Independence of Irrelevant Alternatives?

Dictatorship

Example of a social choice problem, group and alternative

Election, citizens, candidates

How to calculate the Pareto frontier?

Equating MRS, find y/x, use the market clearing condition to replace x2, y2, find y which finds the Pareto frontier.

For (x, t) to Pareto dominate (y, s):

Every individual must prefer weakly (x,t) to (y,s), and at least one of them strictly Every individual can be indifferent between (x,t) and (y,s) except for one who strictly prefers (x,t) to (y,s)

What is universal domain?

Every possible preference profile results in a well-defined (i.e. complete and transitive) social ranking. - a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed.

True or false: The set of strategy equilibria obtained through iterative elimination of dominated strategies is a subset of the set of Nash equilibria.

False

True or false: The Nash Equilibrium must be Pareto efficient

False, no state will be Pareto Optimal if, at least one of the players can get more payoff without decreasing the payoff of any other player. - There are examples of Nash equilibria which are not pareto efficient

True or false: Given some initial endowments and agents' utility functions, a unique competitive equilibrium always exists

False: : it could be that two different allocations that are on the Pareto frontier satisfy budget constraints and market clearing conditions: these would be on tangents to two different sets of indifference curves, that both go through the initial allocation.

True or false: Any allocation on the Pareto frontier in an exchange economy is also a competitive equilibrium.

False: for an allocation to be a competitive equilibrium, it must also be that budget constraints and market clearing conditions are satisfied.

How does a negative externality caused by firm 1 affect competitive equilibrium?

Firm 1 does not internalize the externality and therefore firm 1s production is too high, negatively impacting firm 2's production. This causes inefficiency. In a competitive equilibrium, firm 1s production will be the same as without externality but this will force firm 2 to reduce its optimal level of production. This decreases consumer utility as less products are created

How to calculate the demand functions in a competitive equilibrium?

First write the maximization program, then write lagrangian, calculate FOC1 and FOC2 and BC, FOC1/FOC2, isolate y in BC, find a value for y and plug it in foc1/foc2 and find a value for x, lastly sub x and find a value for y

Arrow's theorem states that:

If a Social Welfare Function has Universal Domain, is Independent of Irrelevant Alternatives and is Pareto efficient, then it is dictatorial

What is a transitive preference ordering?

If an individual prefers a to b, and b to c, then she also prefers a to c. - The property of transitivity of preference says that if a person, group, or society prefers some choice option x to some choice option y and they also prefer y to z, then they furthermore prefer x to z. Formal

Whenever monetary transfers are available, efficient social choice can be achieved by using a utilitarian criterion, explain

If monetary transfers are available then a Pareto efficient choice is always the utilitarian choice. Also if we restrict monetary transfers to be budget balanced, then the utilitarian choice is Pareto efficient.

What is positive responsiveness?

If some individuals change their decision in one common direction, then the aggregate rule does not change in the opposite direction --> if the group decision is indifference or favorable to x, and if individual preferences remain the same except that a single individual changes his/her vote in favor of x, then the group decision should be x

How to know if a function is increasing?

If the first order derivative is bigger than 0

What is neutrality?

If the votes for the two alternatives are reversed, social decision is reversed too.

What do they mean with decentralized?

If we leave the allocation of the agents without intervention from a social planner

What is a mixed strategy equilibrium?

In a mixed strategy equilibrium each player in a game is using a mixed strategy, one that is best for him against the strategies the other players are using. - Example: Penalty kick, the kicker decides to throw the ball left and right with equal probability - Always puts probability 0 on any action that is eliminated by IESDS

How do you make commitment credible?

In absence of an institution that could enforce it, a player may do that by physically restricting her future moves

What is Nash Equilibrium?

In game theory, the result of all players' playing their best strategy given what their competitors are doing. - it is a stability concept--> it is a strategy profile from which no player has an incentive to unilaterally deviate

What is IIA?

Independence of Irrelevant Alternatives

What does indifference mean?

Indifference would mean that a>b and b>a

What are supermajority rules?

Instead of the basis of a majority, a supermajority can be specified using any fraction or percentage which is greater than one-half. (violates neutrality)

What is Iterated Elimination of Strictly Dominated Strategies (IESDS)?

Is one common technique for solving games that involves iteratively removing dominated strategies.

What is the marginal rate of transformation?

Is the number of units or amount of a good that must be forgone to create or attain one unit of another good.

What does the resource constraint do?

It allows writing one consumer's consumption as a linear combination of the others

What does the Pareto weight depends on?

It depends on the distribution factors such as relative wages or population gender ratios and culture

A nash equilibrium is often not unique

It exists under fairly general conditions

What does Walras' law imply?

It implies that equilibrium prices are determined up to scale (the unit of price is irrelevant). Only relative prices are determined in equilibirum

What is the normal form of the game?

It is a way of playing the game in a static way by making all players commit to given actions in the future

What are limitations to implementing quotas?

It is difficult to estimate the correct amount for the quota You need to prevent cheating by firms in order to enforce the quota

What is the edgeworth box?

It is used to analyze the trading of goods. It merges the indifference map between the parties in the trade by inverting one of the agents diagram and allows us to see whether an allocation is Pareto optimal. All individuals maximize their utility.

Why do we use the Lagrange?

It is used to solve optimization problems. It generalizes to more than 2 goods. The third marginal utility should be also equal to λ times the corresponding price.

What is manipulability in social choice?

It may be in the individual's interest to lie depending on how they evaluate the chance of not getting their preferred choice

What does µ replace?

It replaces the minimal utility restriction as the way of indexing points on the Pareto frontier. For any µ there is an equivalent U* and conversely

How do you calculate MRS?

It tells you how much you need to decrease y1 after increasing x1 by one unit while remaining on the same indifference curve.

What does the derivative of a function tell you?

It tells you the change in y that follows from a small change in x.

Equilibrium in strictly dominant strategy

When there is a strictly dominating strategy for each player, which is unique

What is a quota?

Limiting the production and the consumption of a good

Why should MRS=MRT in a competitive equilibrium?

MRS is the demand side of equation while MRT is for the supply side. MRS defines how much a consumer is willing to give up of good X for 1 additional unit of good Y to stay on the same utility level. It is shown by indifference curve. MRS = Price of X/ Price of Y Similarly, MRT is how much a supplier is willing to give up producing good X for 1 additional unit of good Y. It is shown by Production Possibility Frontier. MRT = MC of X/ MC of Y In a perfectly competitive market, equilibrium will take place only when all the parties are better off by making the trade. If a consumer is willing to give up 3 burgers for 1 pizza while supplier is giving up 2 burgers for producing 1 more pizza, economy will not be in equilibrium. Supplier is better off by giving up 3 burgers as it reduces the cost for him, and consumer is better off by giving up 2 burgers for a pizza as he will be left with 1 burger in addition to a pizza. It creates a better trade for both the parties. In equilibrium, either of the parties will switch from what they wish to give up as it is favourable for them.

How to calculate Pareto efficient production externality?

MRT=MRS

Voting

Majority rule More than two choices: pairwise majority voting Plurality rule Borda count

majority rule

Majority rule is a principle that means the decision-making power belongs to the group that has the most members.

The whole Pareto frontier is the curve containing points such that:

Marginal rates of substitutions of the two individuals are equal

Is the Pareto frontier always a straight line between (0,0) and (x,y)?

NO, it can be curved and not even join the two points

Does MRT=MRS with externality?

NO, the competitive equilibrium is inneficient

What is anonymity?

Names do not matter for any permutation.

Does pairwise majority voting satisfy universal domain?

No because of the condorcet paradox: it is possible to find preferences of individuals such that majority voting does not generate a transitive ordering of alternatives.

Can a strategy eliminated by IESDS be a Nash equilibrium?

No it cannot

Does the Borda rule satisfy the Condorcet winner criterion?

No it does not.

Given a production function f, can a quantity y only be produced if it lies on the production frontier y = f(x)?

No, Efficient levels of productions are on the frontier of this set.

Are all Pareto improvements Pareto efficient?

No, Pareto efficient allocations are a subset of all Pareto improvements

Assuming perfect competition, absence of transaction costs and full information, are competitive equilibria a way to resolve externality problems and still obtain a Pareto efficient allocation>

No, assuming the specified conditions are satisfied, you also need to assume that there are no externalities to have a Pareto efficient competitive equilibrium

Assume money transfers are possible. If x is the utilitarian choice, then (x, t) is Pareto efficient.

No, it is true when: - Assume money transfers are possible. If x is the utilitarian choice and t is budget balanced and individually rational, then (x, t) is Pareto efficient. -: Assume money transfers are possible. If x is the utilitarian choice, then there exists some (x, t) that is Pareto efficient.

Is Nash equilibrium the best prediction of how a game will be played?

No, not necessarily

Are Kaldor Hicks improvements a Pareto improvement?

No, you can easily find Kaldor Hicks improvements that are not Pareto

Does Pareto efficiency imply utilitarianism?

ONLY in budget balanced transfers. When money transfers are possible and restricted to be budget balanced, if (x, t) is Pareto efficient, then x is the utilitarian choice.

To find a backwards induction equilibrium, one must:

Observe players' best responses starting at the end of the game, and work their way up to the beginning

What is the hold up problem?

Occurs when a party to a future transaction has to make non-contractible future relationship-specific investments before the transaction takes place Example: Entrepreneur gets an investment from business angel. The next day, the entrepreneur sells his business for under market value, because the amount is still so big so the entrepreneur can retire comfortably, even though the business angel lost money on the deal. - makes commitment less likely

What is Kaldor-Hicks efficiency?

Outcomes that would be Pareto-efficient if there were zero transaction costs are Kaldor-Hicks efficient.

What are the properties of Pareto dominance?

PD defines a social ordering of alternatives. there are no cycles (trasitivity) Pareto property is satisfied IIA is satisfied UD is not satisfied becuase the implied social ordering is not complete

What is Pareto dominance?

Pareto dominated if some other outcome would make at least one player better off without hurting any other player. - Alternative a dominates alternative b if (1) everybody weakly prefers a to b for all i and (2) at least one individual strictly prefers a to b

Which criterion does the Borda rule satify?

Pareto efficiency and Universal Domain

What measures restore efficiency>

Quotas Taxes Changing the market: pollution rights

What do utility changes tell us about Pareto efficiencies and externalities?

Rational optimization is not always Pareto-efficient in the presence of externalities. - Both individuals see their utility improve when the exchange takes place, this is a pareto improvement.

What is sequential pairwise majority voting with a fixed agenda?

Satisfies the Condorcet winner criterion and solves the Condorcet paradox--> Two alternatives are voted on first; the majority winner is then paired against the third alternative, etc

Preference aggregation rule

Social preference ordering decides what outcomes are good for society. The dependence is described abstractly by a preference aggregation rule : Input (preference profile --> F --> output (social ranking) Satisfies the independence of irrelevant alternatives (IIA)

What is a pure strategy?

Strategy in which a player makes a specific choice or takes a specific action--> choosing the option that provides maximum profit, best outcome

Strategic behavior

Strategy proofness (is a sought-after property in social choice functions be- cause it ensures that agents have no incentive to misrepresent their private in- formation at both the interim and ex post stages) also leads to logical impossibilities

What does the prisoner's dilemma show?

That strategic interaction between egoistic rational agents can be detrimental to the collective good

What does Walras' law state?

That the existence of excess supply in one market must be matched by excess demand in another market so that both factors are balanced out. That there is no excess demand or supply

What is the Borda count?

The Borda count is a ranked voting system: the voter ranks the list of candidates in order of preference. So, for example, the voter gives a 1 to their most preferred candidate, a 2 to their second most preferred, and so on. It is complete, transitive and subject to ties.

Strategy-proofness is inconsistent with social choice mechanisms in general, explain

The Gibbard-Satterthwaite theorem says that strategy-proofness implies dictatorship.

What is consumer income?

The amount of income remaining after taxes and expenses have been deducted from wages

What are limitation of implementing a tax to restore efficiency?

The consumer pays for the tax and they do not internalize it - knowing what tax to implement is difficult - they require a lot of knowledge -they are approximations

Observing penalty kicks in real life, one concludes that

The empirical evidence indicates we should account for heterogeneity among players

What is the Condorcet paradox?

The failure of majority rule to produce transitive preferences for society. Majority voting may yield cycles (preferring a>b first , then b>c, but c>a)

What do you call it when there is only one strategy left after IESDS?

The game is called a dominance-solvable game

What is the agenda of voting?

The order in which alternatives are paired

What is Condorcet's jury theorem?

The probability of a correct majority decision Pr{F(v1, ..., vN) = x} is greater than each individual probability. -(so that each voter is less likely to vote incorrectly than correctly), adding more voters increases the probability that the majority chooses correctly and the probability of a correct decision is maximized for a jury of size one.

What is the production set?

The set of production outputs (y1, y2) obtained by varying inputs (x1,x2)

Preference aggregation

The social choice problem individual rationality

What is pairwise majority voting?

The winner of each pairing is the candidate preferred by a majority of voters. Unless they tie, there is always a majority when there are only two choices. The candidate preferred by each voter is taken to be the one in the pair that the voter ranks (or rates) higher on their ballot paper.

Social choice theory main lesson

There is no ideal way of aggregating preferences. All axiomatic constructions yield to dictatorship

Why are externalities problematic in markets?

They cause competitive equilibria to be non-Pareto efficient

What is weighted majority voting?

This happens what some individuals are given more wieght than others (violates anonymity)

What is the market for pollution rights?

This is a market where firms are allowed to buy and sell government-issued licenses granting the holder the right to create a certain amount of pollution.

In a pure exchange economy, free market is the most efficient way to organize trade, explain

This is the first welfare theorem. However, this result breaks down in the presence of frictions or externalities.

How to determine whether the production function is increasing?

To check concavity you take the second order derivative and it needs to be smaller than 0

Suppose firm 1's production imposes a negative externality on firm 2. Then firm 1's production under competitive equilibrium will be:

Too high to be efficient

What does rationality imply for preferences?

Transitivity and completeness of preferences

In sequential games, a backward induction equilibrium is always a Nash equilibrium of the normal form game.

True

True or false: An equilibrium in strictly dominant strategies must be unique.

True

What is pareto property?

Unanimity: If all individuals prefer an alternative a to another alternative b (for every individual i, a i b), then the output social ranking ranks a above b

What are the properties of majority voting (optimality of majority voting)?

Universality, anonymity, neutrality, positive responsiveness

What is the difference between Pareto improvement and Kaldor-Hicks?

Unlike a Pareto improvement, a KH improvement can make some losers and some winners as long as winners gain more than losers. A change in the economy is a KH improvement if it can be turned into a Pareto improvement with some redistributive (budget balanced) monetary transfers Hence, a KH improvement is a potential Pareto improvement.

What is the utilitarian social welfare function?

Utilitarian choice is to give the ticket to the individual with highest WTP. It is also the choice that maximizes total value in society.

What happens to Nash equilibrium when there are chances to learn?

We expect that non-equilibrium profiles will not last, and that the play will eventually converge to a Nash equilibrium

What is the unique Nash Equilibrium?

When after eliminating strictly dominated strategies, there is only one strategy for each player remaining.

Linear/total preference ordering

When it is complete and transitive

What is sequential rationality?

When it is the turn of a player to move, she maximizes her utility conditional on the current history

What is Pareto efficiency?

When no one can be made better off without someone else being made worse off. - An economic state where resources cannot be reallocated to make one individual better off without making at least one individual worse off

What is Pareto efficiency?

When no one can be made better off without someone else being made worse off. An alternative is Pareto efficient if no other alternative Pareto-dominates it

What does Arrow's Impossibility Theorem state?

a mathematical result showing that, under certain assumed conditions, there is no scheme for aggregating individual preferences into a valid set of social preferences -states that there is no fair voting system to determine one's order of preference if the election involves more than two candidates. -->with at least 3 alternatives! (either it is not UD, IIA or Paretian)

What is reciprocity?

a strong human tendency to respond to another's action with similar behavior - contestant are less likely to cooperate if their opponent has tried to vote them off the show

What is the plurality rule?

a type of electoral system where the victory goes to the candidate with the most votes but not the majority necessarily. For ex. if there 3 candidates and one get 34% and the other 2 get 33% the 34% one wins. Example: UK one round elections

What is strategic behavior?

actions taken by firms which are intended to influence the market environment in which they compete. Any market imperfection will have the tendency to be exploited by some agents for their own benefit --> the manipulation

How to rank with Nanson system?

after a Borda count, eliminate all candidates with Borda score above average. The remaining candidates move on to the following round. The winner is the only remaining candidate at the end of this process.

What is the exchange economy?

an economy in which goods are exchanged for money or other goods.

How to calculate the Pareto frontier?

by equating both MRS

how to calculate the production frontier?

combining the two firms' production functions and the resource constraint. Rearranging f1 gives x1 = y 2 1 and the resource constraint gives x2=.... sub this into f2

What is complete preference ordering?

completeness means that when a consumer is choosing between two different options, the consumer can rank them so either, A is preferred to B, B is preferred to A, or they are indifferent between the two. They can always say which option they prefer

How to calculate marginal productivity?

deriving the production function

Assume money transfers are possible. If a choice (x, t) is Pareto efficient, then x is the utilitarian choice

false: Transfers have to be budget balanced

utility function

formula that assigns a level of utility to individual market baskets. the willingness to pay is captured by a utility function

What does Independence of Irrelevant Alternatives mean?

if one candidate (X) would win an election, and if a new candidate (Y) were added to the ballot, then either X or Y would win the election. - Is a condition that states that the relative likelihood of choosing from A from B won't change if a third choice is placed into the mix.

What is an indifference curve?

is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Each point on an indifference curve indicates that a consumer is indifferent between the two and all points give him the same utility.

What are mixed strategies?

is a probability distribution one uses to randomly choose among available actions in order to avoid being predictable

What is a Pigouvian tax?

is a tax on a market transaction that creates a negative externality, or an additional cost - It can lead to a more efficient outcome when markets are inefficient - example: Carbon taxes

What is Walrasian tatonnement or Walrasian auction?

is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. --> adjusting prices can allow for feasible equilibrium

What is a pure strategy equilibrium?

is an action profile with the property that no single player i can obtain a higher payoff by choosing an action different from ai, given every other player j adheres to aj.

Does dictatorship satisfy the Condorcet winner?

no

Does sequential pairwise voting with a fixed agenda satisfy Pareto property?

no

Is an externality always a negative effect?

no there are also positive externalities

What do you call a preference ordering that is not complete?

partial

What does transitivity rule out?

preference cycles

What is approval voting?

same as plurality rule but each voter may give a point to more than just one candidate.

How to rank with the Hare system?

several rounds of plurality voting are organized; at the end of each round, the candidate with the fewest votes is eliminated, and the remaining candidates move on to the following round. The winner is the only remaining candidate at the end of this process.

What is the Gibbard-Satterthwaite Theorem?

states that every voting rule is manipulable, except possibly in two cases: (1) if there is a distinguished voter who has a dictatorial power, or (2) if the rule limits the possible outcomes to two options only. -Suppose that there are at least three alternatives and that for each individual any strict ranking of these alternatives is permissible. Then, the only unanimous (Pareto) and strategy-proof social choice function is a dictatorship.

Given an initial endowment (and assuming it is possible to improve upon the initial endowment), the set of all Pareto efficient allocations is graphically defined as:

the Pareto frontier restricted to area of Pareto improvements

What is the marginal rate of substitution (MRS)?

the amount of a good that a consumer is willing to consume compared to another good, as long as the new good is equally satisfying.

Pareto efficiency is equivalent to utilitarianism

the best policy is the one that maximizes a weighted sum of individual utilities

What is an externality?

the effect of production or consumption of goods and services imposes costs or benefits on others which are not reflected in the prices charged for the goods and services being provided. - it is a source of inefficiency

What is a budget constraint?

the limit on the consumption bundles that a consumer can afford. - It is a straight line passing through (x1,y1) with slope −p/q.

What is the Pareto frontier?

the line representing the possible divisions of the maximum feasible benefit (represents all Pareto efficient solutions)

How to calculate the MRT?

the marginal cost of producing another unit of a good divided by the resources freed up by cutting production of another unit.

willingness to pay

the maximum amount that a buyer will pay for a good

What is a Condorcet winner?

the person who would win a two-candidate (pairwise) election against each of the other candidates in a plurality vote. May not always exist

What is the Coase Theorem?

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. If there are no or small transaction costs, property rights are well-defined and tradable, then voluntary negotiation will lead to efficiency and the initial allocation of rights does not matter for efficiency.

Given an initial endowment, (and assuming it is possible to Pareto-improve upon that initial endowment) the set of Pareto improvements over the initial endowment is graphically defined as:

the space between the consumers' indifference curves that pass through the initial endowment

What is game theory?

the study of how rational agents (individuals forms, insitutions) behave in strategic situations

How to know if the agent's preferences are single-peaked?

the utility funcitons concavitiy should show that there is a hump

How do you derive an implicit function?

we consider y as a function of x and then we use the chain rule to differentiate any term consisting of y. Now to differentiate the given function, we differentiate directly w.r.t. x the entire function