Week 9 Flashcards
What is behavioural economics?
Behavioural economics attempts to incorporate more realistic psychological assumptions into Economics
What 2 realistic assumptions do we try to incorporate in behavioural economics?
- People are less than fully rational: they make mistakes
- People’s preferences differ from those typically assumed by economists
Give 2 example of the idea that people make mistakes?
People think that a coin that lands Heads four times in a row is more likely to be biased in favour of Heads than it actually is
Likewise, they think that a mutual-fund manager who outperforms the market four years in a row is more likely to be talented than she actually is
What is meant that people make different preferences?
It is mistake to think that rational people are selfish, they dont always try to maximise their ultitiy functions
What is Altruism and give an example?
People caring postively about others well being, e.g. peopel care about their own money and other people’s money.
We are now going to answer the question whether Alturism affects economic behaviour in the market place, to do so what are we going to assign consumers and producers? (THIS IS A MARKET WITH NO ALTURISM)
Consumers, each with value v, trade with sellers with cost c: • at price p, buyer earns v - p and seller p - c ( we assume sellers have same cost of producing)
Classical economics thinks of consumers trying to maximize v - p(consumer surplus) and sellers p - c ( producer surplus)
What would be the equilbirum in this market with no Alturism when Consumers, each with value v, trade with sellers with cost c: • at price p, buyer earns v - p and seller p - c • Classical economics thinks of consumers trying to maximize v - p and sellers p - c?
iF THEY BUY THEY GET V, BUT PAY V , AS THIS CONSUMER HAS V = P = C.
Lets say consumers didn’t only care about themselves but cared about others, they want to maxmise their altruistic ultity function which is what?
n v-p+a(p-c), where a is how much she cares about the seller, and 0
Suppose that a consumer wants to maximize the altruistic utility function v-p+a(p-c), where a is how much she cares about the seller, and 0
Lets now just say that a=1/2 • When buyer cares half as much about seller as about herself, then giving seller £1 costs buyer £0.50 worth of utility, is this worth it?
(-£1 for buyer + (1/2)x£1 for seller)<0
you give £1 to seller ( so minus), but gains half a pound , but less than 0, so this buyer is not willing to forgo the pound to give to seller, even though they care about the seller
Suppose that a consumer wants to maximize the altruistic utility function v-p+a(p-c), where a is how much she cares about the seller, and 0
Lets now just say that a=1/2 • When buyer cares half as much about seller as about herself, then giving seller £1 costs buyer £0.50 worth of utility,
(-£1 for buyer + (1/2)x£1 for seller)<0
As we can see it is not worth it what can we say?
The equilibrium does not change!
- Like before, the price will be p=c!
- The marginal consumer has v=p=c
- This consumer’s utility is v-p+a(p-c)=0 (p-c equals 0 and v-p equals 0, as we assume the marginal consumer is v=p=0
and also they are still indifferent between buying and not buying
TO show why The equilibrium does not change!
- Like before, the price will be p=c!
- The marginal consumer has v=p=c
- This consumer’s utility is v-p+a(p-c)=0
Show this?
At p = c we have the same marginal consumer, one with v =p= c
○ For this consumer: v-p+a(p-c)=c-c+a(c-c)=0
all we are doing is subbing in
Prove that any consumer with value V-C>0 will buy a good
and any consumer with value V-C<0 will not buy the good?
as:v-c+a(c-c)= v-c > 0 ( they have a positive kick when they consume good
(v-c is posititve, p-c = c-c which is 0
as:v-c+a(c-c)= v-c < 0
(v-c is negative, there surplus is negative, price is above willingness to pay
What are some insights in the market of alturism ( or people care more about their own welfare as they do about others)
• Trading behaviour looks identical whether or not people are altruistic!
What would happen if A was bigger than 1 in an alturistic market (people care more about sellers than themselves)?
TBA
Lets see what happens with moral hazard when we have alturists in a patnership, but first how does the diagram look with no alturisim? ( define total marginal beneift, what is it, what is theh efficient level of effort, and where does the patner, exert effort)
The total marginal benefit was 1, when they exerted 1 unit of effort that translated to 1 more unit of production of the company.
We deduced the efficient thing to do is exert effort ei = 1
But infact the patner doesn’t look at the total, they only internalise half of the production, because they share with the other person, so they will exert where there PMB = MC, which is half.
What was the key takeaway in the patnership problem from week 7, when there was moral hazard?
The efficient thing to do, is if the person worked where MC = MTB, but it in actual fact, because there is a moral hazard issue, they do not internalise all of the effect on production of the firm, they work less.
Lets see how alturism affects a patnership, first of all does alturism affect the total marignal benefit?
No it doesn’t affect total marginal benefit, as it doesn’t relate to preferences of incentives, when they exert a certain level of effort, they produce 1 more unit of output.
Lets see how alturism affects a patnership, what does Alturism change?
Is how the partner perecives there marignal beneift.
What happens to the private marginal beneift in the patnership problem when they patner is an alturist?
The private marginal beneift will increase, your not only getting half of the production of the firm, ,they are internalising A x 1/2 of the production of the other person, as long as A is strictly positive. This also implies alturist effort will be higher
How much does the alturist increase production by , when there is moral hazard and people are producing efforts < efficient level?
This depends on the parameter A ( how much do they internalise the payoff of the other person.
What is the summary of the lessons learned about patnerships with moral hazard and alturism?
As we saw, in partnerships, partners exert less than the efficient level of effort – they “free ride” - because they receive only half of the marginal benefit of effort (with their partner receiving the other half)
• But when partners care positively about each other’s share, it’s as if each received more than one-half the benefits from her effort, which increases their desired effort level
What is another way to model alturism?
Game theory
Suppose that each player cares 1/10 as much about the other person’s exam score as her own.
Compute the new payoff matrix?
WHAT IS THE EQUILIBRIUM
Assuming they are rational, and alturistic they will play not prepare, not prepare.
Suppose that each player cares 4/5 as much about the other person’s exam score as her own.
Draw payoff matrix
and what is equilibrium?
Now prepare strictly dominates not preparing.
How can we explain using alturism, what is the relationship between an increase in payoff in prepare and alturism?
As the payoff increases from prepare, more people will prepare, depending on the degree of alturism.
How can we show recoprical alturism, using prepare not prepare scenario, suppose that the payoff of alturism is 4/5?
As you can see the altursim is conditioned on the fact that the other player prepares.
Lets say i want to contribute to charity, the question is should i contribute to both charities or focus on one? So what would a warm glow do?
You dont really care about how this money translates to the benefit of society, you just get the warm glow feeling of contributing, so why not split contribution.
Which charity has the higher marginal beneift for a pure alturist? ( 1.2 bn is budget for charity A and 600m for charity b?
The marginal benefit of Charity A is the slope the fact linear function
For charity B if they draw the same line for the slope of charity A, we see theh slope is the same, but when we look at 600m, the slope is higher,
so it is better off to spend your money in charity A if you care about outcome
Person 1 and Person 2 run a business
The value of output is Y=e1+e2
They share Y equally,
Marginal cost equals ei
When each person gets (1/2)Y=(1/2)(e1+e2)
Partners are altruistic: Each partner cares about their own share but also put a weight of a half on other’s share
- Suppose each partner is an altruist who puts a weight of a on her partner’s share. For what value of a will the partners exert the efficient level of output?
(1/2)Y+(1/2)(1/2)Y = (3/4)Y = (3/4)(e1+e2 ),
a = 1/2
the equation is there share add the weight they put on patner times there share.
The private marginal benefit is 3/4 ( derative or (3/4)((e1+1) + e2 ) -(3/4)((e1+e2 ) = (3/4)
The effcieny level of effort
MC = PMB
ei = 3/4
The PMB is higher when they not only care about their own share but the other patners share.
Person 1 and Person 2 run a business
The value of output is Y=e1+e2
They share Y equally,
Marginal cost equals ei
When each person gets (1/2)Y=(1/2)(e1+e2)
Partners are altruistic: Each partner cares about their own share but also put a weight of a half on other’s share
- Suppose each partner is an altruist who puts a weight of a on her partner’s share. For what value of a will the partners exert the efficient level of output?
(1/2)Y+(a)(1/2)Y = (½+(a)×½)(e1+e2 )
The altruist’s private marginal benefit will be higher when a is higher!
For what a will (½+(a)×½)=1? For a=1 we have (½+(a)×½)=1! And effort will be efficient!
A must equal 1.
B is correct
Which of the following are true in the new game?
a. B,B is a Nash equilibrium.
b. B,S is a Nash equilibrium.
c. S,B is a Nash equilibrium.
d. S,S is a Nash equilibrium.
e. There is a mixed strategy Nash equilibrium in which each player plays each action with probability one-half.
A and D, e is wrong you don’t have to calculate the mixed strategy to notice that it isn’t symmetric, so the probability of randomising is not 1/2
Which of the following are true in this game?
a. For any level of altruism of a player, his/her payoff from one player playing B and the other S will always be zero.
b. For some level of altruism of a player, his/her payoff from one player playing B and the other S will be higher than zero.
c. Some levels of Altruism will change the Nash equilibria in pure strategies in this game.
d. Different levels of Altruism will change the Nash equilibria in mixed strategies in this game.
A and D
Problem set
a. What are the Nash equilibria of the game above when played by two Egoistic players? Explain your answers.
In the game above, for each player, the action defect strictly dominates the action cooperate. No rational player ever plays a strictly dominated action. In other words, cooperate is never a best response (for whatever belief the player might have about what her opponent will do). Therefore, there cannot be any Nash equilibrium in which a player plays cooperate!
b)Write down the matrix of the game above when two Altruistic players play this game. What are the pure strategy Nash equilibria of this game? Explain your answers.
c. Write down the matrix of the game above when two Fully Altruistic players play this game. What are the pure strategy Nash equilibria of this game? Explain your answers
There are now two pure strategy equilibria:
- Row player defects, column player cooperates. This is an equilibrium because both players get 8 which is the most that they can hope to get in the game. Therefore, none of them has a strictly profitable deviation!
- Column player defects, row player cooperates. This is an equilibrium because both players get 8 which is the most that they can hope to get in the game. Therefore, none of them has a strictly profitable deviation!
There is also a mixed strategy equilbria
Looking at column player:
Payoff from cooperate: q×6+(1-q)×8
There is also Mixed strategy nash equilbrium q=p=2/3
A) two egoistic
The quick way to answer: In the game above, for each player, the action defect strictly dominates the action cooperate. No rational player ever plays a strictly dominated action. In other words, cooperate is never a best response (for whatever belief the player might have about what her opponent will do). Therefore, there cannot be any Nash equilibrium in which a player plays cooperate!
b) two alturistic players
Therefore now we have two pure strategy Nash equilibria: 1. Both players cooperate. This is an equilibrium as given that the other player cooperates, a player gets (6.3×7+6.3)/7 if they cooperate but less, 50/7 if they defect. Therefore both players are best responding and so this is an equilibrium.
- Both players defect. This is an equilibrium as given that the other player defects, a player gets 16/7 if they defect but less, 2 if they cooperate. Therefore both players are best responding and so this is an equilibrium
c) Fully alturistic players
Note that the payoffs have changed and now cooperate strictly dominates defect for each player. Therefore the only Nash equilibrium is for both players to choose cooperate.
