Strategy, Altruism And Cooperation PDF

8 STRATEGY, ALTRUISM AND COOPERATION Textbook reference: The Economy, Unit 4 GAME THEORY – POSSIBLE OUTCOMES Sometimes social coordination would lead to a better payoff than what is achieved with self- interest pursuit  But how to coordinate? Multiple solutions, and ev...

8 STRATEGY, ALTRUISM AND COOPERATION Textbook reference: The Economy, Unit 4 GAME THEORY – POSSIBLE OUTCOMES Sometimes social coordination would lead to a better payoff than what is achieved with self- interest pursuit  But how to coordinate? Multiple solutions, and everyone agrees one outcome is better but can get stuck in an equilibrium with a lower payoff  Coordination issue again Multiple solutions, but one is better for one player, and another is better for the other player Sometimes everything goes right  The best payoff for everyone is achieve in equilibrium Free ride  A player can benefit from the contributions of the others, with a smaller (or sometimes zero) contribution from oneself HOW TO COORDINATE? Altruism Willingness to bear costs to benefit others Government policies Taxes or subsidies directed to change payoffs Institutions (formal or informal) that take decisions based on the “common good”  EXAMPLE: COMPETITORS SETTING PRICES Nike and Adidas are competing for consumers and can decide whether to set high or low prices for their products Nash equilibrium = (Low price, Low price) Playing Low Price is a dominant strategy  EXAMPLE REVISITED: COMPETITORS SETTING PRICES Now consider the following scenario: Both firms set their prices twice a year: fall/winter collection and spring/summer collection So they play this game twice Would that change the equilibrium? does not change anything Can they achieve a cooperation so that both players will play High Price?  HOW TO SOLVE REPEATED GAMES When the number of repetitions is known by the players, we use backwards induction Backwards induction: Iterative process to determine a sequence of optimal actions start at the end of te game until we reach to the start Solve one repetition at a time Start from the last repetition of the game, and identify what would be the optimal strategy at the last point of the game Using this information, determine what would be the optimal strategy at the second-to-last time that the game is played And keep going backwards until the first round of the game  EXAMPLE REVISITED: COMPETITORS SETTING PRICES Backwards induction: In the last time the game is played (round 2), both players know that the game will not be played again when you know when the game is going to end, … Hence, they do not fear any possible punishment or retaliation by the other player in the next round Each player will choose their best response Both players will play Low Price  EXAMPLE REVISITED: COMPETITORS SETTING PRICES Backwards induction: In the second-to-last time the game is played (round 1), both players know that in round 2 (final round) they will both play Low Price Hence, they do not fear any possible punishment or retaliation by the other player in the next round Each player will choose their best response Both players will play Low Price  EXAMPLE REVISITED: COMPETITORS SETTING PRICES Both players will play Low Price in rounds 1 and 2 of the game Games with a known number of repetitions end up with the same equilibrium strategy as one-shot games  EXAMPLE REVISITED: COMPETITORS SETTING PRICES What if the number of repetitions is unknown? Then there is the possibility of sustaining the cooperative outcome Tit-for-tat strategy: each participant mimics the action of the other player after cooperating in the first round If the other player plays Low Price, then play Low Price in the next round If the other player plays High Price, then play High Price in the next round ifafter you deviate , you benefit for one round but that you lose because they all choose low prices adn instead of 35 they both earn 20  EXAMPLE: CONTRIBUTION TO PUBLIC GOODS In Economics, public good is a good that is: Non-rival in consumption: use by one person does not inhibit use by others public park is for everyone Non-excludable: cannot exclude from use  EXAMPLE: CONTRIBUTION TO PUBLIC GOODS Laboratory experiment that mimic the costs and benefits from contribution to a public good in the real world In groups of 10 people, participants play 10 rounds of a public goods game Each participant is given 20€ in each round, and then they play the following game: Each participant chooses (in secret, and without communicating with others) to put any integer number (between 0 and 20) of their €’s in a box Each participant keeps for themselves whatever amount they did not put in the box For every euro contributed to the box, each person in the group receives 0.40€ That is, for every euro you give, 0.4€ comes back to you, and 0.4€ to each other participant After each round, the participants are told the contributions of the other members of their group For example, if everyone puts 5€, your payoff will be 15 + 0.4*(5 * 10) = 35 But if you put 0 and everyone else puts 5, then you get 20 + 0.4 *(5*9)= 38 How much would you want to contribute (put in the box)? EXAMPLE: CONTRIBUTION TO PUBLIC GOODS  EXAMPLE: CONTRIBUTION TO PUBLIC GOODS Empirical patterns of behavior over time: People are not necessarily selfish Contributions are not zero (despite this being the dominant strategy) Contributions decrease over time It is likely that contributors decreased their level of cooperation once they observed that others were contributing less than expected and were therefore free riding on them  EXAMPLE: CONTRIBUTION TO PUBLIC GOODS Twist: What if we add the possibility of punishment? Punishers are kept anonymous They can make others pay 3€, but they have to pay 1€ to punish others EXAMPLE: CONTRIBUTION TO PUBLIC GOODS  EXAMPLE: CONTRIBUTION TO PUBLIC GOODS Contributions increased when there is the opportunity to punish free riders The punishment of others can be a form of altruism, because it costs something to help deter free riding, which is detrimental to the wellbeing of most members of the group The public goods game, like the prisoners’ dilemma, is a situation in which there is a potential gain for everyone if they coordinate and engage with others in a common project Example: carbon emissions Kyoto Protocol / Paris Agreement  NEGOTIATION Negotiation can be a part of allocating resources Consider the following experiment: Anne and Betty find a 10€ note in the street, and play a game to divide the note Anne proposes to give Betty an (integer) amount between 0 and 10, and Anne keeps rest Betty says yes or no to the proposal If Yes, the proposal is implemented If No, they leave the 10€ in the street (that is, no one gets to keep it) What is the smallest offer Betty would accept? If you were Anne, how much would you offer Betty?  EXPERIMENT: MAIN FINDINGS Results depend on context and social norms Students in the US are much more likely to accept unfair offers than Kenyan farmers Key questions to understand the results: What is a fair split? How do we deal with situations that we consider to be unfair?  EXPERIMENT: MAIN FINDINGS Farmers (Kenya) How do proposers behave? How much do they offer the other player? Proposers in both groups offer the split that maximizes their payoff, given responder’s probability of accepting the offer SEQUENTIAL GAMES That was an example of a sequential interaction Sequential game: a game in which players do not choose their strategies at the same time, and players that choose later can see the strategies already chosen by the other player Framework: Game tree: a graphical representation of a dynamic game Nodes (except final): decision makers have to make a choice Edges: actions at the decision nodes Final nodes: payoffs  EXAMPLE Graphical representation of the Proposer game using a game tree Two players: Proposer and Offer (5,5) Offer (8,2) Respondent The Proposer makes an offer to Responder Responder the Respondent Accept Reject Accept Reject If the offer is rejected, both players get nothing (5,5) (0,0) (8,2) (0,0) If it is accepted, the split is implemented  HOW TO SOLVE THIS GAME? Because Anne (Proposer) moves first, she can decide which equilibrium the players reach When games are played sequentially, we can solve them using backwards induction Start at the last node At each node, the player picks the action that maximizes her own payoff Only consider actions on the optimal path Threats become credible  EXAMPLE What is the equilibrium? Proposer Let us use backwards induction Start from the second stage and Offer (5,5) Offer (8,2) find the Responder’s best responses If Proposer offers (5,5), the Responder Responder Responder’s best response is to Accept (5 vs 0) Accept Reject Accept Reject If Proposer offers (8,2), the Responder’s best response is to Accept (2 vs 0) (5,5) (0,0) (8,2) (0,0) The Responder has a dominant strategy: Accept  EXAMPLE Backwards induction Proposer Now move backwards to the first stage and find the Proposer’s best responses Offer (5,5) Offer (8,2) The Proposer anticipates that the Responder will choose Accept to Responder both offers Responder The Proposer decides between Accept Accept Reject Reject getting 5 or 8 She prefers 8 The Proposer offers (8,2) (5,5) (0,0) (8,2) (0,0) Equilibrium = (Offer(8,2), (Accept, Accept)) left to the right  WHAT DO WE THINK ABOUT THIS? As before start from a purely self-interested person The minimum acceptable offer is 1, as 1 > 0 This is anticipated by proposer who, being self interested, maximizes her money proposing 9 But what if preferences are different? Fairness concerns? Social norms? Perhaps there is a social norm that unearned money has to be shared We dislike deviations from the social norm, and might want to punish them REMEMBER THE EMPIRICAL FINDINGS Farmers (Kenya)  EXAMPLE REVISITED Change the payoff structure to Proposer change the predictions of the Offer (5,5) Offer (8,2) model Data can inform how we set up the Responder Responder model Accept Reject Accept Reject Now the Responder gets upset if (5,5) (0,0) (8,-5) (0,0) she receives an offer that is unfair (negative to change the payoff structure) number is considered unfair utility  EXAMPLE REVISITED What is the equilibrium? Proposer Backwards induction Offer (5,5) Offer (8,2) Find Responder’s best responses, then find Proposer’s Responder Responder Equilibrium = (Offer(5,5), Accept Reject Accept Reject (Accept, Reject)) (5,5) (0,0) (8,-5) (0,0)  ANOTHER EXAMPLE – GROUP WORK REVISITED What is the equilibrium of this Betty sequential game? Backwards induction High effort Low effort Find Player 2’s best responses, Adam Adam then find Player 1’s High effort Low effort High effort Low effort Equilibrium = (High Effort, (High Effort, Low Effort)) (18,18) (12,16) (16,12) (14,14)  WHAT WE HAVE LEARNED Reciprocity Inequality aversion: dislike outcomes in which some individual receives (a lot) more than others Altruism and fairness matters People are fast learners from repeated situations Social norms matter Social norm: an understanding that is common to most members of a society about what people should do in a given situation 9 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT Textbook reference: The Economy, Unit 5 POWER AND INSTITUTIONS How do we organize society and economic relationships? Important concepts: Power: the ability to do and get the things we want, even if in opposition to the intentions of others Institutions: written and unwritten rules that govern interactions of people in a joint project and the distribution of its products rules written and unwritten That is, institutions set the rules Some maybe unwritten, such as social norms Rules set the incentives: economic reward or punishment that changes the benefits and costs of alternative courses of actions Incentives can be monetary or non-monetary Hence, institutions influence the power and thus the economic outcomes of interactions EXAMPLES OF INSTITUTIONS Property rights Competitive markets Banking system and financial markets Social norms Legal system Corruption Democracy Government bureaucracies Cultural traditions POWER AND INSTITUTIONS Important concepts: Bargaining power: the extent of a person’s advantage in securing a larger share of the economic rents made possible by an interaction labor market : workers union Allocation: a description of who does what, the consequences of their actions, and who gets what as a result /outcome That is, the outcome of an economic interaction RULES OF THE GAME: INSTITUTIONS Remember a game specifies: 1. Players 2. Strategies 3. Payoffs payoff matrix = utility Institutions must specify: 1. Who are the players 2. What can each player do, and when 3. After all is said and done, who gets what: allocations From an institution to a game: Allocations + preferences of players = payoffs Preferences define how much each player likes each allocation EVALUATING INSTITUTIONS Institutions’ influence upon the balance of power in economic interactions affects the fairness and efficiency of the results of those interactions Suppose that we want to compare two possible allocations, A and B, that may result from an economic interaction Can we say which allocation (A or B) is better? EVALUATING INSTITUTIONS To evaluate economic institutions and the outcomes of economic interactions (allocations) we will focus on two criteria: 1. Efficiency objective definition of efficiency and fairness is more subjective 2. Fairness Fairness is subjective, that is, what is fair for one person may not be fair for another What is an efficient allocation? EVALUATING INSTITUTIONS: EFFICIENCY An allocation is Pareto efficient if there is no other feasible allocation where at least one player is better off and nobody is worse off That is, if there is no other allocation where all are at least as well-off and someone improves Pareto dominant: an allocation A Pareto dominates allocation B if at least one player would be better off with A than B, and nobody would be worse off On the other hand, an allocation is Pareto dominated if there exists an allocation where all are at least as well-off and someone improves Pareto move: change from one allocation to another where at least one player is better off and no one is worse off If an allocation is Pareto efficient, then there are no available Pareto moves  EXAMPLE Two farmers, Anil and Bala, can use either integrated pest control (IPC), or the pesticide Toxic Tide Nash equilibrium = (Toxic Tide, Toxic Tide) if player 2 plays ipc,player 1 plays toxic if player 2 plays toxic , player 1 plays toxic tide Playing Toxic Tide is a dominant strategy payoff is 2,2  EXAMPLE Anil and Bala are self-interested, preferring allocations with a higher payoff for themselves Let us use a graph to represent each possible allocation in the pest control game How can we compare different allocations in terms of efficiency?  EXAMPLE How does allocation (I, I) compare to allocation (T, T)? Does one allocation Pareto-dominates the other? allocation i i paredo dominates t t, because both are better off The allocation (I, I) lies in the rectangle northeast of (T, T), so both players prefer (I, I) (I, I) Pareto-dominates (T, T) (T, T) is Pareto dominated by (I, I)  EXAMPLE How does allocation (T, T) compare to allocation (T, I)? Does one allocation Pareto-dominates the other? If Anil uses Toxic Tide and Bala IPC, then Anil is better off but Bala is worse off than when both use Toxic Tide The Pareto criterion cannot say which of these allocations is better  EXAMPLE Remember: an allocation that is not Pareto-dominated by any other allocation is called Pareto efficient That is, if an allocation is Pareto efficient, then there is no alternative allocation in which at least one agent (player) would be better off and nobody worse off both are better off in ii instead of tt ( ii pareto dominates tt) ii is pareto efficient what is the difference between nash equilibrium and pareto efficient? na Are there any Pareto-efficient allocations in this example?  EXAMPLE Are there any Pareto-efficient allocations in this example? Pareto-efficient allocations: (I, T), (I, I), and (T, I) Allocation (T, T) is not Pareto efficient because it is dominated by (I, I) ALTERNATIVE CRITERION Pareto efficiency is a very demanding criterion A weaker version of it is the notion of potential Pareto improvement (if redistribution is possible) Pareto Potential Improvement: change from one allocation to another, where the gain of the player who is improving is enough to compensate the loss of the player who is getting worse  pareto dominant when evaluiting two allocations pareto efficient will need that allocation never be pareto dominanted by the other EXAMPLE Are there any potential Pareto improvements in this example? Consider (T, T) and (T, I) There is a potential Pareto improvement from (T, T) to (T, I) Anil’s payoff increases by 2 (from 2 to 4), while Bala’s payoff decreases by only 1 (from 2 to 1) Remember that the stronger Pareto criterion we used before could not say which of these allocations was better HOW TO THINK ABOUT EFFICIENCY? There can be more than one Pareto-efficient allocation In the example we saw (pest control game), there are three: (I, I), (I, T), and (T, I) The Pareto criterion does not tell us which of the Pareto-efficient allocations is best That is, it does not rank all the Pareto-efficient allocations: (I, I), (I, T), and (T, I) The Pareto criterion does not always allow us to say one allocation is better than the other Even by the Pareto criterion, a Pareto-efficient allocation is not always better than a Pareto-inefficient one We know that (T, I) is Pareto efficient, and (T, T) is not. But if you compare the two, (T, I) does not Pareto- dominate (T, T) IS EFFICIENCY ENOUGH? We might care about other criteria when evaluating allocations For instance, efficiency has nothing to do with fairness Fairness: a way to evaluate an allocation based on one’s conception of justice WHAT IS FAIR? Remember the experiment from last week (ultimatum game) Anne and Betty find a 10€ note in the street, and play a game to divide the note Anne proposes to give Betty an (integer) amount between 0 and 10, and Anne keeps rest Betty says yes or no to proposal If Yes, the proposal is implemented If No, they leave the 10€ in the street (that is, no one gets to keep it) WHAT IS FAIR? Do you think the allocations below are fair or unfair? Anne proposes to give Betty 1 and to keep 9 to herself Anne proposes to give Betty 1 and to keep 9 to herself. We know that Anne just lost her job, while Betty has a highly paid job Anne proposes an even split, where each of them gets 5 Anne proposes an even split, where each of them gets 5. But that only occurred because Betty forced and threatened Anne to offer an even split What is considered fair may depend on several factors: The outcome (allocation) itself, the context, and how the allocation came about (the rules of the game, whether someone was forced to do something or not), etc.  EVALUATING INSTITUTIONS: FAIRNESS Allocations can be judged unfair because of: How unequal the allocations are: in terms of income, for example, or subjective wellbeing These are called substantive judgements of fairness How the allocations came about: for example, by force, or by competition on a level playing field These are called procedural judgements of fairness Legitimacy of voluntary exchange: Were the actions resulting in the allocation the result of freely chosen actions by the individuals involved? Or was fraud or force involved? Equal opportunity: Did people have an equal opportunity to acquire a large share of the total to be divided up? Or were they subjected to some kind of discrimination or other disadvantage because of their race, sexual orientation, gender, or who their parents were? Deservingness: Did the rules of the game that determined the allocation take account of the extent to which an individual worked hard?  WHAT DOES ECONOMICS HAVE TO DO WITH FAIRNESS? Different people may have different evaluations on how fair or unfair an outcome or a situation is Economics cannot eliminate disagreements about questions of fairness (neither does philosophy nor political science) But Economics can help clarify: How the rules of the game (and institutions) affect the degree of inequality Trade-offs between dimensions of fairness Example: do we have to compromise on the equality of income if we also want equality of opportunity? How public policies address concerns about unfairness Institutions shape the fairness of allocations in the economy WRAPPING UP 10 PROPERTY AND POWER: MUTUAL GAINS AND CONFLICT Textbook reference: The Economy, Unit 5  LOOKING BACK Production functions Feasible set Preferences  A MODEL OF CHOICE AND CONFLICT Rules of the game (institutions) matter to determine final allocations Consider a sequence of scenarios involving two characters, Angela and Bruno Rule 1 (initial situation): Angela, a farmer, works the land and gets everything she produces Rule 2: Bruno appears, he does not farm but wants part of the harvest, and can force Angela to work for him Rule 3: The rule of law replaces the rule of force. Bruno can no longer coerce Angela to work. But Bruno owns the land and, if Angela wants to farm his land, she must agree to pay him part of the harvest Rule 4: Rules change, and Angela (and other farmers) achieve the right to vote and pass legislation that increases Angela’s claim on the harvest Question: how does efficiency and distribution change?  RULE 1 Rule 1: Angela works the land and gets everything she produces (initial situation) Angela owns the land Optimality condition: there are no constraint to make (trade off MRS = MRT angela is willing to make is equal to the trade off she is constrained to mak by the production function) Optimal choice: 16h of free time (8h of work) 46 bushels of grain  A MODEL OF CHOICE AND CONFLICT Rule 1 (initial situation): Angela, a farmer, works the land and gets everything she produces Angela owns the land Rule 2: Bruno appears, he does not farm but wants part of the harvest, and can force Angela to work for him Forced labor  FEASIBLE FRONTIER AND ALLOCATIONS Since the technology is the same as in Rule 1 and Bruno is not working, the feasible frontier remains unchanged total production Each point on or within the frontier represents an allocation At allocation D Angela has 16 hours of free time Of the 46 bushels of grain she produces, Bruno how the prpoduction is split between ana keeps 31 bushels and gives 15 to her and bruno Point A is also an allocation, in which he gives her all the grain  FEASIBLE SET what is the bare minimum so that she still works for him (if she refuses, then production for bruno is 0) 𝐼𝐶 is Angela’s reservation indifference producing at 62, ana would want everythhing curve if she refuses to work with bruno and does something else. same utility level as her outside option It shows combinations that would give Angela the happy if he proposes more than that ( feasible set ) same level of utility she would expect to get from unhappy if it outside disobeying Bruno and doing something else (her next best alternative) instead That is, each point on this indifference curve gives Angela the smallest level of utility such that she would still work for Bruno lowest allocation she would be willing to stay and work for bruno Bruno’s feasible set: Bruno can choose any allocation between Angela’s reservation indifference curve and the feasible frontier  minimum pay she would require to work a given HOW WILL BRUNO CHOOSE? amount of hours Bruno wants as much grain as possible for himself He will choose a feasible allocation on Angela’s reservation indifference curve This way, he gives her enough utility not to rebel and escape What is Bruno’s optimal choice? mrs=mrt  HOW WILL BRUNO CHOOSE? Bruno’s optimal choice: Allocation D: Angela works 8h and produces 46 bushels of grain (point A), out of which Bruno keeps 31 bushels and gives 15 to texto texto Angela Optimality condition: MRS = MRT MRS: slope of Angela’s reservation indifference curve MRT: slope of the feasible frontier  HOW WILL BRUNO CHOOSE? The maximum Bruno can get occurs where MRS = MRT To the left of 16 hours of free time (where Angela works more), MRS > MRT any point to the left of d is not optimal (more valuable the hours are for her) - opportunity cost of free time Bruno could benefit from giving Angela a bit more free time: her output of grain would fall, but the grain she would require to be no worse off (that is, to remain on IC1) would fall by even more So Bruno would get more for himself To the right of 16 hours of free time (where Angela works less than eight hours), MRS < MRT Bruno can benefit from giving Angela less free time The extra grain she would produce is more than the additional grain she would require to remain on IC1  A MODEL OF CHOICE AND CONFLICT Rule 1 (initial situation): Angela, a farmer, works the land and gets everything she produces Angela owns the land Rule 2: Bruno appears, he does not farm but wants part of the harvest, and can force Angela to work for him Forced labor Rule 3: The rule of law replaces the rule of force. Bruno can no longer coerce Angela to work. But Bruno owns the land and, if Angela wants to farm his land, she must agree to pay him part of the harvest Employment contract Take it or leave it contract (Angela cannot negotiate the terms of the contract)  FEASIBLE SET What happens to the feasible set? Feasible frontier? only angela is available to work and she did not change her techniques Unchanged Angela’s reservation indifference curve? Angela’s reservation indifference curve is now outside option os better than before higher (shifts up) Angela’s reservation option in Rule 3 is much better than in Rule 2: her utility from finding work elsewhere is higher than the utility she could expect if she attempted to revolt or escape  HOW WILL BRUNO CHOOSE? bruno keeps less Bruno gets the most grain where the slope of Angela’s reservation indifference curve (MRS) is equal to the slope of the feasible frontier (MRT) MRS = MRT Offers the following contract to Angela: she works 8h and receives a wage of 23 bushels Allocation L: Angela works 8h and produces 46 bushels of grain (point A), out of which Bruno keeps 23 bushels and gives 23 to Angela  A MODEL OF CHOICE AND CONFLICT Rule 1 (initial situation): Angela, a farmer, works the land and gets everything she produces Angela owns the land Rule 2: Bruno appears, he does not farm but wants part of the harvest, and can force Angela to work for him Forced labor Rule 3: The rule of law replaces the rule of force. Bruno can no longer coerce Angela to work. But Bruno owns the land and, if Angela wants to farm his land, she must agree to pay him part of the harvest Employment contract Take it or leave it contract (Angela cannot negotiate the terms of the contract) Rule 4: Rules change, and Angela (and other farmers) achieve the right to vote and pass legislation that increases Angela’s claim on the harvest Bargaining in a democracy  RULE 4 Suppose that Angela and others who work on neighboring farms lobby the government to improve their conditions They want working hours for farm laborer's restricted to four and a half hours per day They also want to get at least the same amount of grain as under the voluntary take-it-or- leave-it contract agreement in Rule 3, which was 23 bushels The government agrees to the demands of the farm laborer's  FEASIBLE SET What happens to the feasible set? Feasible frontier? Unchanged Angela’s reservation indifference curve? Shifts up (Angela’s reservation utility has risen) The feasible set is now more limited (small shaded area) Bruno must offer a contract in the shaded area: on or below the feasible frontier, with no more than four and a half working hours and a wage of at least 23 bushels Allocation L is no longer feasible  ALLOCATION What will be the allocation under Rule 4? Bruno will get the most grain at allocation N Angela works for the maximum number of hours (4.5h) and produces at point M (35 brushels) Angela receives a wage of 23 bushels (minimum wage) Bruno gets 12 bushels If Bruno gave Angela more free time, less gain would be produced, and he would still have to pay her the minimum wage (23 bushels)  EFFICIENCY We saw the optimal allocation under the four different rules Are they all Pareto efficient? What makes an allocation efficient in this setting? To be Pareto efficient, an allocation must have two important properties: MRS = MRT: the MRT on the feasible frontier is equal to the MRS on Angela’s indifference curve If MRS ≠ MRT, then a Pareto improvement is possible if Angela’s work hours are changed If MRS = MRT, then no Pareto improvement is available mrs>mrt bruno could get more without harming angela No grain is wasted: all the grain produced is consumed by Angela or Bruno If there is waste, then a feasible increase in consumption would make at least one of them better off If there is no waste, then if one consumes more, the other would get less  PARETO EFFICIENCY Pareto efficiency curve: the set of all Pareto-efficient allocations In this particular case, it is a vertical line The set of allocations with 16h of free time (8h of work) Key assumption: Angela’s indifference curves for angela to get more/improve. bruno gets less/take are parallel the hit This made the point where MRS equals MRT to always happen at 16h of free time  PARETO EFFICIENCY Which allocations are Pareto efficient? The first three allocations (under rules 1, 2 and 3) are Pareto efficient They all lie in the Pareto efficiency curve Remember that they all satisfy the MRS = MRT condition, and there is no waste How about the allocation under Rule 4?  ALLOCATION UNDER RULE 4 Initial allocation: N Angela works 4.5h and gets 23 bushels Bruno gets 12 bushels Now suppose that the new law allows for a longer workday, if both parties agree Can Angela and Bruno reach a Pareto- efficient contract?  POTENTIAL PARETO IMPROVEMENT UNDER RULE 4 Allocations in the Pareto efficiency curve between points P and R Pareto dominates allocation N At point P, Angela is indifferent between P and N (that is, not worse nor better off), but Bruno gets more bushels (16 instead of 12) At point R, Angela is better off than at point N (point R lies at the northeast of her indifference curve N), while Bruno gets the same 12 bushels (not worse off) At points between P and R, both Angela and Bruno are better off  THE IMPACT OF INSTITUTIONS ON FAIRNESS AND EFFICIENCY Different institutions regarding property rights and labor markets Forced labor, take it or leave it contract, pareto efficient pareto efficient bargaining in a democracy to get minimum pareto efficient wage of 23 bushels and limit daily work not pareto effcient hours to 4.5h, negotiation in a democracy Most allocations were Pareto efficient First, second and fourth cases But how about fairness? subjective HOW DO INSTITUTIONS MATTER? Preferences Bargaining power Allocation (outcome): Institutions who does what & who Reservation option gets what Economically feasible allocations Technically feasible Technology allocations