L18 - Asymmetric Information: Principal Agent I

Question 1

QUESTION

IN all of these relationships there are a number of key characteristics:

Fill in the blacks

1. A principal delegates a task to an….
2. The principal collects all the revenue or wider benefits – he is the…….
3. • However, the agent has control of some decisions. Hence, there is a separation of……
4. • There is a divergence in……

Answer 1

1. A principal delegates a task to an agent
2. The principal collects all the revenue or wider benefits – he is the residual claimant
3. • However, the agent has control of some decisions. Hence, there is a separation of ownership from control
4. • There is a divergence in objectives

Question 2

How can the principal best design a set of invectives to influence the agent?

(Based off last weeks lecture under full information)

Answer 2

Question 3

How is this lecture different to the previous ones?

Answer 3

• Now, we consider some similar questions under asymmetric information.
• This introduces an additional moral hazard problem because the principal cannot observe the agent’s effort.
• Instead of contracting on effort, it will now often be optimal for the principal to offer the agent a bonus conditional on output (or performance).
• As such, this topic can offer a variety of insights into different contracts and the social desirability of payments in the form of bonuses in various markets.
• This is still a highly relevant recent issue in banking,
• . Extending our knowledge of contracts into asymmetric information is also useful for your future careers as employees and as potential future employers.

Question 4

How does asymmetric information effect incentives design?

Answer 4

• Assume now that effort is asymmetric information such that the principal cannot observe the agent’s effort. This generates moral hazard.
• How does this affect the optimal contract and the resulting equilibrium effort?
  
  • Nothing changes if the relationship between effort and output is unique and non-random. Why? The owner can then always perfectly infer the level of effort from the level of output and so they can just contract on output instead of effort.
  • However, things are more difficult if output is determined by effort and a random factor, like the weather or market conditions
• Due to moral hazard, a farmer might now face the incentive to exert low effort and blame the consequent low output on the weather.
• This problem can be easily solved using the franchising solution from the last lectures. By selling the revenue rights to the farmer, the farmer has every incentive to select the optimal effort regardless of whether effort is observed or not, and regardless of the state of the weather.
• However, a further complication arises if the farmer is risk averse.
• Under a franchise, the farmer’s payoffs will be very volatile due to the effects of the weather. As such, he may be unwilling to pay the full value for the franchise. Hence, the potential revenue from franchising may be sub-optimally low for the owner when the farmer is risk averse.
• These specific situations lead us to ‘principal agent games’….

Question 5

How is the principal-agent game structured?

Answer 5

• Incentive Design under:
  
  • asymmetric information
  • stochastic output
  • agent risk aversion
• A Principal (P) wants to hire an Agent (A) to work on a project. Output is observable and contractible, but the effort is not. Output has a random element.
• P offers A a contract specifying a wage, w, and a bonus, b. The wage will be paid in all circumstances; the bonus will only be paid if a successful outcome occurs.
• If A accepts the contract, he chooses effort, e, equal to high (H) or low (L). The high effort has a monetary cost of 1, while low effort costs 0.

**** Note how the Agent’s payments and effort costs both enter the U function

Question 6

In the principal-agent game, what would be the outcome if full information was available?

Answer 6

• Therefore, e+H is socially efficient, and P would like to induce e = H if possible

Question 7

Under the full information benchmark, the states that risk is distributed efficiently, what does this mean?

Answer 7

• The principal is the only one where there is some probability (risk) in the revenue he receives and the agent does not have any
• why is the efficient –> principal is risk neutral so they don’t care either way about it whereas the agent is risk averse, and thus want to avoid it

Question 8

How do we find the optimal contract of the principal-agent game under asymmetric information?

Answer 8

• Under asymmetric information, the Principal can’t contract on effort.
• Further, we also know that franchising may be suboptimal for the Principal due to the Agent’s risk aversion.
• Instead, how can the Principal use a wage and bonus conditional on output, to control the agent’s effort more profitably?

*Need to find out what w and b would be!

• high effort –> the expected payoff of success v failure must be greater than what he can get else where
• and thus the high effort needs to generate a better expected revenue than low effort

Question 9

What are the three steps for solving the principal-agent game under asymmetric information?

Answer 9

1. If b=0, the moral hazard problem will prompt A to shirk and set e=L.
   
   1. Why? From the ICC, he can get the same expected payment of w from exerting high effort as he can from exerting low effort, yet high effort is costly.
   2. Hence, to induce high effort, the P must set a positive value of b. Bonuses can be important and necessary.
      
      1. ​as if you look at the high v low effort constraint, without b it can never be greater than returns putting in low effort and thus leaves no incentive
2. ​The PC must hold with equality under an optimal contract. If not, the P could gain by lowering w while still ensuring participation and high effort. So,
   
   1. EU_A(e=H) = 0.5(w + b -1)^0.5 + 0.5(w-1)^0.5 = U_A(N) = 1
      
      1. if high effort way higher –> principal could just lower-wage down till they are equal, so you are just willing to do the work than go anywhere else
3. Why does the ICC need to hold?
   
   1. Cause Agent is risk-averse he wants to certain wage over the uncertain bonus
      
      1. but he keeps the expected wage bill CONSTANT
      2. the principal can increase an agents utility by increasing wage but lowering bonus yet this does nothing to the average wage bill overall –> exploiting the risk attitudes to the point the ICC condition is equal

Question 10

Under asymmetric information what are the payoffs of the principal-agent game in equilibrium?

Answer 10

• given that w* = 1 and b* = 4

Question 11

What are some features of the optimal contract?

Answer 11

• Note that P imposes some risk on the risk averse Agent by making his payment partially dependent upon output {𝑤, 𝑤 + 𝑏}.
• This is consistent with the use of sharecropping contracts (from last lecture) and gives one explanation for their usage in practice.
• However, from what we said before, imposing risk on the agent is inefficient.
• So why does the Principal do it?
  
  • Some risk is needed to induce the agent to select the efficient effort level and overcome the moral hazard problem. Need 𝑏 > 0.
  • However, by imposing some risk on the agent, the risk-averse agent needs compensating and so this drives up the expected payment
• As a result, in our example, the Principal is worse off under asymmetric information relative to full information. He now gets a payoff of 1 rather than 2.
• However, the agent receives the same payoffs of 1 in both cases.
• Therefore, at the social level, asymmetric information creates welfare losses.
• These are termed as agency costs. –> welfare reduction created by the asymmetric asymmetric - which is leading to inflated payments to compensate the agent for the extra risk

Question 12

What happens under extreme cases of asymmetric information to our optimal contract?

Answer 12

• where the problem of asymmetric information is acute or the risk-aversion of the agent is very strong there may be no incentive to use incentives to bonuses

Question 13

As risk-aversion gets larger what happens to the principal payoff?

Answer 13

• x^a where a controls risk aversion
  
  • So what happens when a gets smaller
• if general owners payoff is
  
  • z- y(b)^1/a
• ^​where z and y are constants, b equals bonus and a = risk aversions
  
  • when a gets smaller, exponent gets bigger and thus bonuses get bigger –> wanted to be compensated more for taking on the same risk
  • owners payoff thus gets smaller as they are paying more out in bonuses
    
    • In some questions this may lead to the wage changing too –> its actually strange that in some cases just change bonuses could be optimal as this are inherently risky in themselves
• if a is sufficiently small it may be possible that the bonus is so expensive that it actually leads to the principal to end up with a negative payoff