Remedies to Moral Hazard by alicejenny

VIEWS: 1 PAGES: 78

									                                    Remedies to Moral Hazard

              Based on "Further topics in moral hazard" by Eric Rasmusen

                                               http://www.rasmusen.org


                                                       June 2012




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   1 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.
       3   Boiling in oil:




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.
       3   Boiling in oil:
       4   Selling the store: the managers buy the …rm in a leveraged buyout.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.
       3   Boiling in oil:
       4   Selling the store: the managers buy the …rm in a leveraged buyout.
       5   E¢ ciency wages.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.
       3   Boiling in oil:
       4   Selling the store: the managers buy the …rm in a leveraged buyout.
       5   E¢ ciency wages.
       6   Tournaments.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.
       3   Boiling in oil:
       4   Selling the store: the managers buy the …rm in a leveraged buyout.
       5   E¢ ciency wages.
       6   Tournaments.
       7   Monitoring: The directors hire a consultant to evaluate the
                    s
           executive’ performance.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Ways to Alleviate Agency Problems

       1   Reputation: Managers are promoted on the basis of past e¤ort or
           truthfulness.
       2   Risk-sharing contracts: The executive receives not only a salary, but
                                  s
           call options on the …rm’ stock. If he reduces the stock value, his
           option fall in value.
       3   Boiling in oil:
       4   Selling the store: the managers buy the …rm in a leveraged buyout.
       5   E¢ ciency wages.
       6   Tournaments.
       7   Monitoring: The directors hire a consultant to evaluate the
                    s
           executive’ performance.
       8   Repetition: Managaers are paid less than their marginal products for
           most of their career, but are rewarded later with higher salaries or
           generous pensions if the career record has been good.
                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   2 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.
           Before he buys insurance his dollar wealth is 0 if there is a theft and
           12 otherwise.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.
           Before he buys insurance his dollar wealth is 0 if there is a theft and
           12 otherwise.
           If he is careful Theft occurs with probability 0.5.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.
           Before he buys insurance his dollar wealth is 0 if there is a theft and
           12 otherwise.
           If he is careful Theft occurs with probability 0.5.
           If he is careless the probability rises to 0.75.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.
           Before he buys insurance his dollar wealth is 0 if there is a theft and
           12 otherwise.
           If he is careful Theft occurs with probability 0.5.
           If he is careless the probability rises to 0.75.
           He is risk averse, and other things equal, he has a midl preference to
           be careless, a preference worth some small amount ε.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.
           Before he buys insurance his dollar wealth is 0 if there is a theft and
           12 otherwise.
           If he is careful Theft occurs with probability 0.5.
           If he is careless the probability rises to 0.75.
           He is risk averse, and other things equal, he has a midl preference to
           be careless, a preference worth some small amount ε.
           The insurance company is risk-neutral.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Insurance


           The agent is considering buying theft insurance for a car with a value
           of 12.
           Before he buys insurance his dollar wealth is 0 if there is a theft and
           12 otherwise.
           If he is careful Theft occurs with probability 0.5.
           If he is careless the probability rises to 0.75.
           He is risk averse, and other things equal, he has a midl preference to
           be careless, a preference worth some small amount ε.
           The insurance company is risk-neutral.
           Competition among insurance companies.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   3 / 20
  Observable Care




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   4 / 20
  Observable Care



           If the agent chooses Careful,

                                 π a = 0.5U (12                   x ) + 0.5U (0 + y    x)
                                 πp      = 0.5x + 0.5(x                  y)




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)        June 2012   5 / 20
  Observable Care



           If the agent chooses Careful,

                                 π a = 0.5U (12                   x ) + 0.5U (0 + y    x)
                                 πp      = 0.5x + 0.5(x                  y)

           If the agent chooses Careless

                            π a = 0.25U (12                    x ) + 0.75U (0 + y      x) + ε
                            πp      = 0.25x + 0.75(x                    y)




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)        June 2012   5 / 20
  Unobservable Care




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   6 / 20
  Unobservable Care




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   7 / 20
  Unobservable Care




           Partial-insurance (Example: premium of 6 and payout of 8). We can
           think of it in two ways:




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   8 / 20
  Unobservable Care




           Partial-insurance (Example: premium of 6 and payout of 8). We can
           think of it in two ways:
           Full insurance except for a deductible of four (the company pays for
           all losses in excess of four)




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   8 / 20
  Unobservable Care




           Partial-insurance (Example: premium of 6 and payout of 8). We can
           think of it in two ways:
           Full insurance except for a deductible of four (the company pays for
           all losses in excess of four)
           Insurance with a coinsurance rate of one-third. (The insurance
           company pays two-thirds of all losses)




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   8 / 20
  E¢ ciency Wages




   Is the aim of an incentive contract to punish the agent if he chooses the
   wrong action? Not exactly. Rather, it is to create a di¤erence between
             s
   the agent’ expected payo¤ from right and wrong actions, something
   which can be done either with the stick of punishment or the carrot of
   reward. It is important to keep this in mind, because sometimes
   punishments are simply not available




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   9 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.
           The executive accepts the contract, or rejects it and receives his
           reservation utillity of U = 5.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.
           The executive accepts the contract, or rejects it and receives his
           reservation utillity of U = 5.
           The executive exerts e¤ort e of either 0 or 10.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.
           The executive accepts the contract, or rejects it and receives his
           reservation utillity of U = 5.
           The executive exerts e¤ort e of either 0 or 10.
           Both players are risk neutral




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.
           The executive accepts the contract, or rejects it and receives his
           reservation utillity of U = 5.
           The executive exerts e¤ort e of either 0 or 10.
           Both players are risk neutral
                       s
           Corporation’ payo¤: q                     w.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.
           The executive accepts the contract, or rejects it and receives his
           reservation utillity of U = 5.
           The executive exerts e¤ort e of either 0 or 10.
           Both players are risk neutral
                       s
           Corporation’ payo¤: q                     w.
                    s
           Executive’ payo¤: w                    e.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




           Players: A corporation and an executive
           The corporation o¤ers the executive a contract which pays w (q )                          0
           depending on pro…t, q.
           The executive accepts the contract, or rejects it and receives his
           reservation utillity of U = 5.
           The executive exerts e¤ort e of either 0 or 10.
           Both players are risk neutral
                       s
           Corporation’ payo¤: q                     w.
                    s
           Executive’ payo¤: w                    e.
           Nature chooses pro…t according to Table 1.



                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   10 / 20
  E¢ ciency Wages
  The Lucky Executive Game




                                                                   .




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   11 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5
           so his expected wage must equal 15




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5
           so his expected wage must equal 15
           The incentive compatibility constraint is
                         0.5w (0) + 0.5w (400)                    0.1w (0) + 0.9w (400)           10




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5
           so his expected wage must equal 15
           The incentive compatibility constraint is
                         0.5w (0) + 0.5w (400)                    0.1w (0) + 0.9w (400)           10
           which can be written as w (400) w (0) 25, so the gap between
                         s
           the executive’ wage for high output and low output must equal at
           least 25.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5
           so his expected wage must equal 15
           The incentive compatibility constraint is
                         0.5w (0) + 0.5w (400)                    0.1w (0) + 0.9w (400)           10
           which can be written as w (400) w (0) 25, so the gap between
                         s
           the executive’ wage for high output and low output must equal at
           least 25.
           A contract that satis…es both constraints (and binding) is
           w (0) = 7.5 and w (400) = 17.5.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5
           so his expected wage must equal 15
           The incentive compatibility constraint is
                         0.5w (0) + 0.5w (400)                    0.1w (0) + 0.9w (400)           10
           which can be written as w (400) w (0) 25, so the gap between
                         s
           the executive’ wage for high output and low output must equal at
           least 25.
           A contract that satis…es both constraints (and binding) is
           w (0) = 7.5 and w (400) = 17.5.
           But his contract is not feasible if we require w (q ) 0.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           The participation constraint is
                                   0.1[w (0)          10] + 0.9[w (400)                10]   5
           so his expected wage must equal 15
           The incentive compatibility constraint is
                         0.5w (0) + 0.5w (400)                    0.1w (0) + 0.9w (400)           10
           which can be written as w (400) w (0) 25, so the gap between
                         s
           the executive’ wage for high output and low output must equal at
           least 25.
           A contract that satis…es both constraints (and binding) is
           w (0) = 7.5 and w (400) = 17.5.
           But his contract is not feasible if we require w (q ) 0.
           This is an example of the common and realistic bankruptcy
           constraint. (the principal cannot punish the agent by taking away
           more than waht the agent owns in the …rst place)
                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)             June 2012   12 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?
           What can be done is to use the carrot instead of the stick and
           abandon satisfying the participation constraint as an equality.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?
           What can be done is to use the carrot instead of the stick and
           abandon satisfying the participation constraint as an equality.
           All that is needed for constraint (2) is a gap of 25 between the high
           wage and the low wage.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?
           What can be done is to use the carrot instead of the stick and
           abandon satisfying the participation constraint as an equality.
           All that is needed for constraint (2) is a gap of 25 between the high
           wage and the low wage.
           Setting the low wage as low as is feasible, the corporation can use the
           contract
                                   w (0) = 0, w (400) = 25
           and induce high e¤ort.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?
           What can be done is to use the carrot instead of the stick and
           abandon satisfying the participation constraint as an equality.
           All that is needed for constraint (2) is a gap of 25 between the high
           wage and the low wage.
           Setting the low wage as low as is feasible, the corporation can use the
           contract
                                   w (0) = 0, w (400) = 25
           and induce high e¤ort.
           Executive’ expected utility: 0.1(0) + 0.9(25)
                      s                                                                10 = 12.5 > 5. More
           than his reservation utility.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)           June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?
           What can be done is to use the carrot instead of the stick and
           abandon satisfying the participation constraint as an equality.
           All that is needed for constraint (2) is a gap of 25 between the high
           wage and the low wage.
           Setting the low wage as low as is feasible, the corporation can use the
           contract
                                   w (0) = 0, w (400) = 25
           and induce high e¤ort.
           Executive’ expected utility: 0.1(0) + 0.9(25) 10 = 12.5 > 5. More
                      s
           than his reservation utility.
           The corporation’ payo¤ is 337.5 (= 0.1(0 0) + 0.9(400 25)).
                            s




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

           So what can be done?
           What can be done is to use the carrot instead of the stick and
           abandon satisfying the participation constraint as an equality.
           All that is needed for constraint (2) is a gap of 25 between the high
           wage and the low wage.
           Setting the low wage as low as is feasible, the corporation can use the
           contract
                                   w (0) = 0, w (400) = 25
           and induce high e¤ort.
           Executive’ expected utility: 0.1(0) + 0.9(25) 10 = 12.5 > 5. More
                      s
           than his reservation utility.
           The corporation’ payo¤ is 337.5 (= 0.1(0 0) + 0.9(400 25)).
                            s
           Such payo¤ is higher than the one associated to the low e¤ort and:
           195 = 0.5(0 5) + 0.5(400 5).

                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   13 / 20
  E¢ ciency Wages
  The Lucky Executive Game

         So what can be done?
         What can be done is to use the carrot instead of the stick and
         abandon satisfying the participation constraint as an equality.
         All that is needed for constraint (2) is a gap of 25 between the high
         wage and the low wage.
         Setting the low wage as low as is feasible, the corporation can use the
         contract
                                 w (0) = 0, w (400) = 25
           and induce high e¤ort.
           Executive’ expected utility: 0.1(0) + 0.9(25) 10 = 12.5 > 5. More
                             s
           than his reservation utility.
           The corporation’ payo¤ is 337.5 (= 0.1(0 0) + 0.9(400 25)).
                                        s
           Such payo¤ is higher than the one associated to the low e¤ort and:
           195 = 0.5(0 5) + 0.5(400 5).
           Since high enough punishments are infeasible, the corporation has to
           use higher rewards.                       Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org) June 2012 13 / 20
  E¢ ciency Wages


           Executives, of course, will be lining up to work for this corporation,
           since they can get an expected utility of 12.5 there and only 5
           elsewhere




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   14 / 20
  E¢ ciency Wages


           Executives, of course, will be lining up to work for this corporation,
           since they can get an expected utility of 12.5 there and only 5
           elsewhere
           Potential successors would be willing to pass up alternative jobs in
           order to be in position to get this unusually attractive job.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   14 / 20
  E¢ ciency Wages


           Executives, of course, will be lining up to work for this corporation,
           since they can get an expected utility of 12.5 there and only 5
           elsewhere
           Potential successors would be willing to pass up alternative jobs in
           order to be in position to get this unusually attractive job.
           Thus, the model generates unemployment.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   14 / 20
  E¢ ciency Wages


           Executives, of course, will be lining up to work for this corporation,
           since they can get an expected utility of 12.5 there and only 5
           elsewhere
           Potential successors would be willing to pass up alternative jobs in
           order to be in position to get this unusually attractive job.
           Thus, the model generates unemployment.
           The employer pays a wage higher than that needed to attract workers,
           and workers are willing to be unemployed in order to get a chance at
           the e¢ ciency-wage job.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   14 / 20
  E¢ ciency Wages


           Executives, of course, will be lining up to work for this corporation,
           since they can get an expected utility of 12.5 there and only 5
           elsewhere
           Potential successors would be willing to pass up alternative jobs in
           order to be in position to get this unusually attractive job.
           Thus, the model generates unemployment.
           The employer pays a wage higher than that needed to attract workers,
           and workers are willing to be unemployed in order to get a chance at
           the e¢ ciency-wage job.
           To induce a worker not to shirk, the …rm can o¤er to pay a premium
           over the marketclearing wage, which he loses if he is caught shirking
           and …red.


                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   14 / 20
  E¢ ciency Wages



           If one …rm …nds it pro…table to raise the wage, however, so do all
           …rms. One might think that after the wages equalized, the incentive
           not to shirk would disappear. But when a …rm raises its wage, its
           demand for labor falls, and when all …rms raise their wages, the
           market demand for labor falls, creating unemployment. Even if all
           …rms pay the same wage, a worker has an incentive not to shirk,
           because if he were …red he would stay unemployed, and even if there
           is a random chance of leaving the unemployment pool, the
           unemployment rate rises su¢ ciently high that workers choose not to
           risk being caught shirking.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   15 / 20
  Tournaments




           Games in which relative performance is important are called
           tournaments.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   16 / 20
  Tournaments




           Games in which relative performance is important are called
           tournaments.
           Tournaments are especially useful when the principal wants to elicit
           information from the agents




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   16 / 20
  Tournaments




           Games in which relative performance is important are called
           tournaments.
           Tournaments are especially useful when the principal wants to elicit
           information from the agents
           A principal-designed tournament is sometimes called a yardstick
           competition because the agents provide the measure for their wages




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   16 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.
           Independently for each technique, Nature chooses production cost c
           = 1 with probability φ and c = 2 with probability (1 φ).




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.
           Independently for each technique, Nature chooses production cost c
           = 1 with probability φ and c = 2 with probability (1 φ).
           The manager can either choose a technique at random or investigate
           the costs of both techniques at a utility cost to himself of α.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.
           Independently for each technique, Nature chooses production cost c
           = 1 with probability φ and c = 2 with probability (1 φ).
           The manager can either choose a technique at random or investigate
           the costs of both techniques at a utility cost to himself of α.
           The shareholders can observe the resulting production cost, but not
           whether the manager investigates.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.
           Independently for each technique, Nature chooses production cost c
           = 1 with probability φ and c = 2 with probability (1 φ).
           The manager can either choose a technique at random or investigate
           the costs of both techniques at a utility cost to himself of α.
           The shareholders can observe the resulting production cost, but not
           whether the manager investigates.
           The wage contract: w1 if c = 1 and w2 if c = 2.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.
           Independently for each technique, Nature chooses production cost c
           = 1 with probability φ and c = 2 with probability (1 φ).
           The manager can either choose a technique at random or investigate
           the costs of both techniques at a utility cost to himself of α.
           The shareholders can observe the resulting production cost, but not
           whether the manager investigates.
           The wage contract: w1 if c = 1 and w2 if c = 2.
           Manager’ utility: log(w ) if he does not investigate and log(w )
                    s                                                                              α if
           he does.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments


           Let …rm Apex have two possible production techniques, Fast and
           Careful.
           Independently for each technique, Nature chooses production cost c
           = 1 with probability φ and c = 2 with probability (1 φ).
           The manager can either choose a technique at random or investigate
           the costs of both techniques at a utility cost to himself of α.
           The shareholders can observe the resulting production cost, but not
           whether the manager investigates.
           The wage contract: w1 if c = 1 and w2 if c = 2.
           Manager’ utility: log(w ) if he does not investigate and log(w )
                    s                                                                              α if
           he does.
           Reservation utility: log(w ).


                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   17 / 20
  Tournaments
           If the shareholders want the manager to investigate, the contract
           must satisfy the self-selection constraint
           φ log(w1 ) + (1             φ) log(w2 )           [1     (1      φ)2 ] log(w1 ) + (1   φ)2 log(w2 )




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)          June 2012   18 / 20
  Tournaments
           If the shareholders want the manager to investigate, the contract
           must satisfy the self-selection constraint
           φ log(w1 ) + (1             φ) log(w2 )           [1     (1      φ)2 ] log(w1 ) + (1   φ)2 log(w2 )
           Turning inequality (4) into an equality and simplifying we get
                                           w1
                             φ(1 φ) log( ) = α               (5)
                                           w2




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)          June 2012   18 / 20
  Tournaments
           If the shareholders want the manager to investigate, the contract
           must satisfy the self-selection constraint
           φ log(w1 ) + (1             φ) log(w2 )           [1     (1      φ)2 ] log(w1 ) + (1     φ)2 log(w2 )
           Turning inequality (4) into an equality and simplifying we get
                                           w1
                             φ(1 φ) log( ) = α               (5)
                                           w2
           The (binding) participation constarint is
           log(w ) = [1             (1      φ)2 ] log(w1 ) + (1              φ)2 log(w2 )   α               (6)




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)            June 2012   18 / 20
  Tournaments
           If the shareholders want the manager to investigate, the contract
           must satisfy the self-selection constraint
           φ log(w1 ) + (1             φ) log(w2 )           [1     (1      φ)2 ] log(w1 ) + (1     φ)2 log(w2 )
           Turning inequality (4) into an equality and simplifying we get
                                           w1
                             φ(1 φ) log( ) = α               (5)
                                           w2
           The (binding) participation constarint is
           log(w ) = [1             (1      φ)2 ] log(w1 ) + (1              φ)2 log(w2 )   α               (6)
           Solving equations (5) and (6)
                                                   w1 = w e α/φ
                                                                         α/(1 φ)
                                                   w2 = w e




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)            June 2012   18 / 20
  Tournaments
           If the shareholders want the manager to investigate, the contract
           must satisfy the self-selection constraint
           φ log(w1 ) + (1             φ) log(w2 )           [1     (1      φ)2 ] log(w1 ) + (1        φ)2 log(w2 )
           Turning inequality (4) into an equality and simplifying we get
                                           w1
                             φ(1 φ) log( ) = α               (5)
                                           w2
           The (binding) participation constarint is
           log(w ) = [1              (1        φ)2 ] log(w1 ) + (1           φ)2 log(w2 )     α                (6)
           Solving equations (5) and (6)
                                                   w1 = w e α/φ
                                                                         α/(1 φ)
                                                   w2 = w e
           The expected cost to the …rm is
                                                                                         α/(1 φ)
                                [1        (1     φ)2 ]w e α/φ + (1            φ )2 w e
                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)               June 2012   18 / 20
  Tournaments


           If the parameters are φ = 0.1, α = 1, and w = 1, the values are
           w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   19 / 20
  Tournaments


           If the parameters are φ = 0.1, α = 1, and w = 1, the values are
           w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
           Quite possibly the shareholders decide it is not worth making the
           manager investigate.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   19 / 20
  Tournaments


           If the parameters are φ = 0.1, α = 1, and w = 1, the values are
           w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
           Quite possibly the shareholders decide it is not worth making the
           manager investigate.
           But suppose that Apex has a competitor, Brydox, in the same
           situation




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   19 / 20
  Tournaments


           If the parameters are φ = 0.1, α = 1, and w = 1, the values are
           w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
           Quite possibly the shareholders decide it is not worth making the
           manager investigate.
           But suppose that Apex has a competitor, Brydox, in the same
           situation
           The shareholders of Apex can threaten to boil their manager in oil if
           Brydox adopts a low-cost technology and Apex does not.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   19 / 20
  Tournaments


           If the parameters are φ = 0.1, α = 1, and w = 1, the values are
           w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
           Quite possibly the shareholders decide it is not worth making the
           manager investigate.
           But suppose that Apex has a competitor, Brydox, in the same
           situation
           The shareholders of Apex can threaten to boil their manager in oil if
           Brydox adopts a low-cost technology and Apex does not.
           If Brydox does the same, the two managers are in a prisoner’ s
           dilemma, both wishing not to investigate, but each investigating from
           fear of the other



                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   19 / 20
  Tournaments




                s
           Apex’ forcing contract speci…es w1 = w2 to fully insure the
           manager, and boiling-in-oil if Brydox has lower costs than Apex




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   20 / 20
  Tournaments




                s
           Apex’ forcing contract speci…es w1 = w2 to fully insure the
           manager, and boiling-in-oil if Brydox has lower costs than Apex
           The contract need satisfy only the participation constraint that
           log(w α) = log(w ), so w = 2.72 and Apex’ cost of extracting the
                                                          s
                   s
           manager’ information is only 2.72, not 4.185.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   20 / 20
  Tournaments




                s
           Apex’ forcing contract speci…es w1 = w2 to fully insure the
           manager, and boiling-in-oil if Brydox has lower costs than Apex
           The contract need satisfy only the participation constraint that
           log(w α) = log(w ), so w = 2.72 and Apex’ cost of extracting the
                                                          s
                   s
           manager’ information is only 2.72, not 4.185.
           Competition raises e¢ ciency, not through the threat of …rms going
           bankrupt but through the threat of managers being …red.




                                                     Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen (http://www.rasmusen.org)   June 2012   20 / 20

								
To top