Week8 - Principal Agent Problems & Performance Pay

• what are the characteristics of a principal


  i. standard profit maximiser

  ii. can be though of as a firm owner

  iii. utility function: Up = f(π)
• what is the utility function of an agent

  Ua = g(w,e)

  
  

  utility is increasing: g'(w)>0, g"(w)<0

  effort is decreasing: g'(e)<0, g"(e)<0
• what is the conflict of interest between principals and agents


  principals implicitly want to maximise effort for a given wage

  
  

  agents want to minimise effort subject to wages
• what is the role of information asymmetry in this context


  if effort is perfectly observable then there's no issue as firms can contract on effort such that w = ße

  
  

  ß is the return on effort that workers require to compensate them for the disutility of working

  
  

  but effort isn't perfectly observable so agents know their effort and principals do not
• how do optimal contracts with full information work


  the principal offers wage wfor effort level ewhich leads to the profit maximising level of production:

  
  

  MC = w

  MR = pMPl

  
  

  so the profit maximising wage - effort combination is:

  
  

  w= pf(e)

  
  

  the agent accepts this offer forming a labor contract (w,e)
• what does information asymmetry cause


  its an incentive for the agent to renege on eand provide e instead where e<ecausing a moral hazard problem
• what effects does a moral hazard problem have on production and why may this occur


  the firm observes that q<q* since workers renege on effort

  
  

  this could be because of shirking but if there is any stochastic element, E, to production i.e. q = g(e, E) then the worker can always claim that they got a bad draw of E i.e. bad weather, bad week etc
• how can firms resolve the moral hazard problem


  i. franchising and self-employment: could sell the rights to a manager or agent i.e. taxi drivers rent cabs for a shift and keep the fares

  
  

  ii. incentive schemes: performance pay, commission etc
• explain algebraically how performance related pay schemes work


  output is an increasing function of effort and some unobservable random shocks:

  
  

  Q = f(e, E)

  
  

  worker utility is a decreasing and concave function of effort and a positive function of wages:

  
  

  Uw = g(e, w)

  Up = h(π)

  
  

  workers cost of effort:

  
  

  C = c(e) where c'(e) > 0 ; c"(e) > 0
• what are the two key predictions of PRP

  i. the stronger the incentive the greater the effort

  ii. trade off between risk and incentives
• what is the relationship between random shocks and incentives


  when random shocks are important, incentives will be weak
• explain algebraically how piece rates work


  agents can be paid by time (input) such that w = s

  
  

  or paid according to output, receiving some rate b for each unit of output

  
  

  jobs are not pure piece rates so:

  
  

  w = s + bQ

  
  

  so agent chooses effort and Q to maximise compensation net of the costs of the effort given Q, C(Q):

  
  

  net compensation: s + bQ - C(Q)

  
  

  equilibrium defined by Qwhere MC(Q) = b

  
  

  provided that s + bQ ≥ C(Q*) + U0
• what do indifference curves look like associated with wages and effort


  they are convex and upward sloping as wages increase utility and effort reduces it

  
  

  so an improvement of combination occurs when the indifference curves move closer to the wages on the vertical axis
• what happens regarding indifference curves when there are no risks


  the worker exerts ead produces Qon a piece rate

  
  

  the piece rate (w = s + bQ) is tangent to the indifference curve
• what is the participation constraint

  s + bQ≥ C(Q)
• how do piece rates lead to higher output

  if agents were paid a flat salary, s, which is horizontal, the indifference curve would be tangent to this curve along the lowest part of the IC

  
  

  since piece rate wages are at a slope of b, they are tangent to indifference curves at a higher point, increasing output
• what is the derivation of maximising profit and equilibrium


  choose s and b to maximise profit : π(Q) = R(Q) - (s + bQ)

  
  

  subject to the participation constraint : s + bQ ≥ C(Q)

  
  

  equivalent to maximising: π(Q) = R(Q) - C(Q)

  
  

  setting MR(Q) = MC(Q) which determines Q*

  
  

  workers set MC(Q*) = b

  
  

  so in equilibrium: MR(Q*) = b

  
  

  and then s = bQ- C(Q)

  
  

  this ensures just enough for agents to participate
• derive and explain a more general contract where Q is risky


  Q is risky when it depends on effort and luck

  
  

  workers may be reluctant to pay s to get a big b

  
  

  so firms could offer insurance to workers:

  
  

  pay s' if Q falls below Q0 and bQ+S if Q>Q0

  
  

  this has some behavioural consequences and just cause the piece rate to be non-linear

  
  

  (refer to powerpoint for graph)
• illustrate how compensation schemes measure the variable that drives performance, Q in this case


  regarding w = s + bEffort + E, a high b will give a strong incentive to provide effort

  
  

  but it also transfers uncontrollably risk to workers as the scheme is effectively w = bQ, hence:

  
  

  w = s + bEffort + bE
• illustrate how risks and incentives play a part in incentive schemes


  suppose Q = e + E and an agent is risk averse

  
  

  the firm observes Q but not e, and compensation is s + bQ = s + b( e + E )

  
  

  in other words, its paying a piece rate on the random and non-random component of output

  
  

  in an employee is risk averse then costs > C(e)

  
  

  so the firm has to compensate the agent for the effort of making Q and carrying the risk

  
  

  a bigger b improves incentives but also raises the riskiness of earnings

  
  

  s' might help here as it limits the downside risk which increases the likelihood of RA workers participating

  
  

  so there's a tradeoff between reducing the risk that RA agents carry and the effort that can be extracted from the worker
• why don't firms just pay a higher base salary / why not just set s' higher as insurance


  i. like all insurance, may lead to moral hazard if agents have any control over risk of production

  
  

  ii. insured agents may take higher risks

  
  

  iii. adverse selection: a higher salary cet par, the more likely lower ability agents will want to enter the firm
• what is the correlation between high and low ability workers and work based on piece rates and salary

  high ability workers will prefer piece rates and low ability workers will prefer salary

  
  

  this may lead to agents sorting across firms according to ability
• why does sorting matter

  harder working/ more able/ more risk seeking workers will choose contracts where hard work is well rewarded

  
  

  so we can't just compare output under piece rates with output under salary to find effective incentives
• briefly explain the issues with piece rates


  i. skimping on quality and use of excessive materials - fear of diminished quality means piece rates will only be used where precise quality standards can be established and easily monitored

  
  

  ii. changes in technology or product lines - tech may make it easier to produce Q for a given effort. may put piece rates out of line with opportunity cost

  
  

  iii. ratchet effect - incentive not to reveal true opportunity cost i.e. pretending a task is harder than it is

  
  

  iv. injuries - overworking

  
  

  v. risk - large exogenous shocks may make it impossible to have a piece rate which meets the participation constraint

  
  

  vi. measurement of output - some jobs are to costly to observe output
• how do bonuses work


  w = s + bonus where,

  
  

  bonus = f( a1, b1, c1)

  where these are a list of performance criteria

  
  

  the difference is that these could be objective (hitting certain targets) or subjective (evaluations of performance)
• what is the possible explanations as to why bonuses have grown so much over the past few years


  i. changes in technology has increased productivity from high ability. PRP allows for this to be rewarded leading to higher wage differentials
• why are CEO's paid so highly and why do they get paid proportionally s much in performance pay

  i. principal-agent setup : CEO's get paid according to how well the firm is doing and hence may align interests of agents and principals

  
  

  ii. but they may also have the power to directly influence the structure of their pay

  
  

  iii. the key debate is not whether they should be paid variable pay but whether actual practices represent some optimal contracting outcome or expropriation of managerial rent
• explain the reason as to why individual incentive schemes might be inefficient

  i. output shocks - could either be an idiosyncratic component specific to the agent or an aggregate component affecting all agents

  
  

  an optimal incentive schemes should try to filter out common risks from individual compensation contracts

  
  

  this would reduce risks and increase the power of incentives
• how could you filter out common shocks

  i. compare output between agents working on the same/similar projects - Relative Performance Evaluation