Asymmetric information Flashcards
What is moral hazard?
hidden action
Give an example of moral hazard with a plumber?
Employing a plumber
Your boiler breaks down
You employ a plumber to Öx your boiler
The plumber knows a lot more about how to Öx boilers than you do
You need to be sure that the plumber takes the right actions and does
not charge you too much
What is the problem here in this plumber example?
It is you not the plumber who you employ who bears the cost of doing a bad job.
How is there a moral hazard problem in finance?
Traders take risks on behalf of investors.
What is adverse selection?
Economic situation which some agents hold private information that is not known to others ( hidden information)
e.g. buying a second hand car ( you want to buy a car, you want know if its reliable, you find and one and the owner tells you its reliable( the owner may be lying), as you are not an expert you cannot check for yourself, so you need trust in owner)
What are moral hazard and adverse selection a problem of?
Asymmetric information.
Why doesn’t everyone know everything?
Its costly and impossible for everyone to know everything ( hence we have a division of labour for specialisation.
What are the implications of moral hazard?
It can have implications for both efficiency and equity.
What is the best way to model moral hazard and what are we going to model?
Principal agent problem and we are going to look at the optimal compensation problem.
So with the optimal compensation problem who is the principal and agents and what are we interested in?
1) A principal: who designs a contract
2) And agent: who is contracted with
We are interested in the design of optimal contracts where
1) the actions of the agent cannot be monitored directly
Now the principal cannot observe the effort of the agent,
What can the outcome of the task be?
What is the princpal payoff ( don’t include costs) if success and failure.
How do we show what the agents effort can be and what is the cost function for agent, and what does this effort mean and why is effort not always 1?
Effort creates a disulitiy with a quadratic cost function
Assume that the agent has no wealth so cannot be punished
(financially) for failure
But she can be rewarded for success.
To perform the task, the agent is therefore offered what? and what else does she have?
Firstly we are going to look at full information benchmark ( what does this mean) what does this mean for the 2 part contract the agent gets?
The principal can contract on the amount of effort that the agent puts in. Putting e although doesn’t guarantee success. This means you don’t have to give bonus.
What is the payoff which makes the agent participate in the contract for full information benchmark, how is the cost function affected what is the lowest possible wage??
What this shows that the higher i contract on effort i have to pay a higher wage, so that it at least = outside option. SO WAGE MUST = OUTSIDE OPTION.( THIS IS THE LOWEST WAGE POSSIBLE)
What is the princpal payoff with full information benchmark, where there is no bonus, but the princpal pays a wage ( rearrange the payoff from last flashcard, to solve for w and substitute in princpals payoff)
Probability of success X expected payoff - W.
We want to find the optimal effort level with full information benchmark, so how do we do this ( HINT using princpals payoff)?
Maximise principals payoff utility with respect to e and then = 0 then find out what e is.
So e = pie/c ( which is the optimal amount of effort i would want agent to put if i could observe the agents effort.)
Let c = 10 and π = 8
Then what is optimal effort?
Why didn’t we choose effort level = 1
If i choose effort level = 100 it would be too expensive.
What is incentive compatibility and why does it matter ?
refers to the idea that we know there is asymmetric information but princpals must anticipate this when making contracts. It matters because you would be naive to think that if i you could make a normal contract and you will get what you want without an incentive for the agent.
So suppose principal cannot observe effort and the agent gets a fixed wage and a bonus depending on success of task, what is the agents ultity function and what is the optimal level of effort now?
Fixed wage + probability of getting bonus x bonus - cost of effort.
What is now the princpals payoff now without full information? knowing that he has to pay a bonus and fixed wage and profit/ payoff depends on success.
What does the princpal also have to respect, so the agent doesn’t turn down contract. What is the tradeoff here for princpal?
Effort depends on b, but paying more b means improving performance but reducing princpals payoff if success.
So we want the contract to be incentive compatible, so given the princpal cannot the agents effort subisutute the incentive compatible level of effort into the the principals payoff and the agents payoff ( sub e = b/c where you see e)
So step 2, what are we trying to maxmise in the to find the optimal contract when there is moral hazard? Do we need wage?
Step 2: Maximize the principalís payo§ subject to the agent getting
at least u
By plotting the agent and princpals ultity as a function of level of bonus paid, what 3 observations can we make ?
1) Utility for the agent is increasing in B.
2) The optimal level of bonus that maximises princpal payoff whilst trading off the fact that you are paying for more effort, but getting more for it is the stationary point.
3) As b goes over the optimal b the princples ultity is falling as a larger share of the bonus is going to agent
What are the 2 cases we want to look at for the optimal contract when such that we maxmise the blue function subject to the agent getting at least a level of utility u.
Case 1 where the outside option is not binding
Case 2 where the outside option is binding.
What does outside option is not binding in comparison to the outside option is binding?
Outside option is not binding = you will not commit to outside option and show up and do task.
Outside option is binding - the agent chooses whether u take the project
Lets look a case 1 when the outside option is not binding. Maximise the principals payoff to and find the optimal bonus when a incentive compatible contract and when will this solution. ( W=0). When will the agent agree to this too.
We know the agents payoff so we sub in b such that its > or equal to u.
SO THE BONUS MUST BE GREATER THAN outside option.
Show here case 1, ( HINT WE KNOW THAT THE OUTSIDE OPTION IS LESS THAN OPTIMAL BONUS THAT MAXMISES PRINCPLES PAYOFF?
As the outside option is less than optimal bonus pie/2, this is the solution to the the princpal agent problem because the agent gets the next best alternative but its optimal to pay as you get the benefit. So no need to worry about outside option.
So we have established that ig c = 10 and π = 8, then what is level of bonus in case 1 we established, when will this be the solution tooo and what is the level of effort of successful completion? What is the problem here?
Because of imperfect information things are not working as well with full info, even though you are dealing optimally with best contract, success is only 0.4.
With case 2 would the bonus of pie / 2 be sufficient to persuade agent to work? What can we think of the outside option as? ( optimal bonus)
No. So the outside option is a high demand market opportunity, so the
princpal has to increase the bonus to get the agent to work for them
So we know that for case 2 the bonus is not enough, the principal needs to pay a higher bonus than this, but not give too much money, so what does he do?
He gives a bonus such that is equal to outside option, then rearrange to find this bonus.
Explain case 2 on diagram?
1) U upper bar is very high, so you get bonus to it, and we see bonus is high and effort is high as a resul, but this gives princpal a lower utility.
What would be the level of bonus and how does that relate to princpal. what is the level of success?
Most profit goes to agent, but effort is higher
e = b/c
What are the implications of all of this?
Naturally the economy has inequality, which is needed in society because of moral hazard, people are paid more than others, despite doing same roles due to demand.
Compare Case 1 and 2 with full info ( don’t have to ) ?
Interesting question suppose that there was 2 identical principals competing for the same agent and the outside option will be high what will happen and Profit is higher than bonus?
The outside option is getting so high that the the princpals pay agents all the profit, meaning that the inefficiency associated with moral hazard goes away. ( Basically you have to give agent all profit as bonus to get to the efficient level of effort when there was perfect information.
If there are more agents than princpals, is there competition and what is optimal effort levels?
Because the outside option doesn’t really exist or carry weight, the alternative is unemployment, hence the effort level will be the same of that in case 1.
So we are now going to look at moral hazard in teams, so in teams what is success determined by, hence what is rewards determined by?
Suppose that there are 2 team members A & B.
Probability of success depends on both team members, so you cant observe individual effort but team,
We want to incorporate intrinsic motivation in our model, so what is the notation we are going to use to show a physic reward you get( HINT its a function of B. and decreasing function)
why a decreasing function? the more you pay me, the less motivated i am to do a task?
What is the utility function of an agent with intrinsic motivation and what is effort? and how can we interpret it ?
If u(b) is positive you put more effort into the task because the pyshic benefit associate with task
How does effort depend on b?
(hint you take derative with respect to b?
Supposing the u(b is a decreasing function>
So now we want to look at how intrinsic motivation affect incentives, so suppose that know what u(b) and that alpha reflects the degree of crowding out ( the higher, the more you think money has a negative effect upon you) , so by subbing this into the princpals payoff and and finding option bonus, what can we say about the bonus when there is intrinsic motivation.
If alpha( the degree of crowding out is high then you don’t use incentives at all.
By plotting the expected utlity as a function of bonus what can we extract here?
Intrinsic motivation shifts the up the utility of principle and agent as the agents gets pleasure from putting effort in.
The principal utility function shifts up as he gets benefits from intrinsic motivation, as he gets more effort per unit of bonus,
Finally as you can see the optimal level of bonus us one the left to what we had without intrinsic motivation.
(ADVERSE SELECTION MODEL) What is the utility from having a peach and what is the utility of a lemon.
As consumers cannot observe whether it is. a peach or not, what is going to be the market price?
( ADVERSE SELECTION PROBLEM) What will you denote as to show whether you decide or not to buy a good or service, and what is the probability of buying a good in the market that is a peach.
What is therefore the expected utility of consumer?
What if you buy a lemon?
if § = 0 then your expected utltiy comes from income
the probabily of buying a good thats a peach is little delta
If you buy a lemon without knowing you get 0 utlitiy so your expected utility is just -p + m
( ADVERSE SELECTION PROBLEM) When you do buy a good a good § E {0,1]
you will always buy the good when your valuation exceeds the price
(ADVERSE SELECTION PROBLEM) Suppose u is distributed with distribution function G (u) What is the demand such that all people who value the good are willing to take risk to buy it.
(ADVERSE SELECTION PROBLEM) What are the 2 kind of suppliers and how many suppliers are there?
(ADVERSE SELECTION PROBLEM) Now lets look at the case with full information, so we know each type of producer picks a price P for peach producer and L for lemon producer, With full information will there be any lemons sold and y and therefore what is the demand function?
(ADVERSE SELECTION PROBLEM) How does the diagram look like when there is full info?
Everyone who has a valuation of u>c will buy the good and no one will be able who wants the good not to get it.
(ADVERSE SELECTION MODEL) ( iMPERFECT INFO SO CONSUMERS KNOW THAT 2/3 ARE PEACH AND 1/3 ARE LEMON) 1) As firms are all charging the same price, what does it mean for consumers. 2) As lemon mimics price of peach will they make a profit? and can peach producers make a profit. 3) As consumers know that 2/3 of the time they are buying a peach, when will they have a peach? 4) what is now the demand for a peach and how does that compare to the full information case.
So what is happening in short, is that price hasn’t changed but t
some failing goods are being traded in equilibrium with those with the highest valuation.
(ADVERSE SELECTION MODEL WITH IMPERFECT INFO) What is the consequences of this? ( HINT THINK ABOUT AS WE ARE LOOKING AT ONE POPULATION SIZE, HENCE REPRESENTATIVE CONSUMER, THINK ABOUT CULUMATIVE DISTRUBTION OF U?
If no one has a valuation higher than U<3/2C because of the risk is too high buying lemon then market collapses completely
Why is this consequence pareto inferior compared to full information and how does the case of imperfect information look on a price and quantity diagram? What does it mean for lemon producers ?
Lemon producers can make a profit and enter in the market
So we are going to look at how guarantees solve the adverse selection problem, so with guarantees when will consumer buy the good supposing that P = C? Does a peach producer ever have to pay for guarantee?
The peach producer never had to pay the guarantee and so produces at that price.
Will a lemon producer offer b at price C, when will he not and how might they get found out?
Hence if guarantees are high they make no profit and leave the market.
So suppose consumers pay sigh to become informed before they shop when will i do this/HOW MUCH WILL I BE WILLING TO DO THIS?
I will be willing to pay for that information if the increase value of buying a peach over a lemon, is sufficient to compensate me for the cost of doing it.
Due to people be willing to pay for information if the extra value compensates the cost, then there are 3 possibilities of people. If the cost of being unformed > cost of being informed then what will happen? How does the diagram look?
Then people will get informed and demand but the extra cost does reduce demand but there is less efficiency than from no infomation ( those you good the good at C, but will not buy the good at sight + c
