Ch 14 Agency

Principal-Agent Relationship

• Principal owns an asset

• Agent works on principal’s behalf to preserve on enhance the value of the asset

• Problem - the agent’s interests can diverge from that of the principal

Example

• Smith and Jones enter into an agreement to provide auto repairs

• Smith provides tools and a shop

• Jones provides labor

• Suppose the relationship is initially 50-50

Example

• Either could be the firm’s “owner”

• Both the tools and the worker combine to fix an engine in a team effort

• Smith and Jones need each other to produce auto repair

Example

• The individual contributions of each cannot be determined

• Thus, an individual member could “shirk”

• The resource owners in the team need to be monitored.

• But, by whom? Who has the greater incentive to monitor

Who is to be the monitor?

• The party with the least incentive to shirk

• The least mobile party

Who is to be the monitor?

• For efficiency- the party central to all contracts

Example

• In exchange for monitoring: this factor is the “residual claimant”

• Thus, it must be able to commit to guarantee all other factors that they will be paid

• Thus, capital has become known to be the “owner” of the firm

Math Example

• Suppose that there is no team production and that workers can be costlessly monitored

• Workers utility function U = (I - e2)

• Worker requires a minimum $1,000 just to show up for work

Math Example

• Workers utility function U = (I - e2)

• Worker requires a minimum $1,000 just to show up for work

• You must compensate me if you want me to exert more effort

• Ex: If e =10, then I =$1,100 Ex: If e = 100, then I = $11,000

Math Example

• Thus, the cost to the firm is:

• C = 1000 + e2

Math example

• Suppose the firm benefits by $100 for each extra unit of effort made by the employee

• B = 100e

The Firm’s Goal

• Pick a level of effort that maximizes profit

• Profit = 100e - (1000 + e2)

• dProfit/de = 100 - 2e

• Set equal to zero, yields e =50

Profit Maximization

• By paying the worker 1000 + 502 = $3,500 the firm offers the incentive to the worker to put forth 50 units of effort

• The firm could elicit more effort from the worker, but the additional cost would exceed the additional benefit

Profit Maximization

• By paying the worker 3,500

• the firm gets 50 units of effort

• This yield 5,000 in gross benefits to the firm

• Less the 3,500 salary to the worker

• yields a profit of 1,500

Problem

• If the salary is fixed at $3,500 and “e” is not costlessly observable

Problem

• If the salary is fixed at $3,500 and “e” is not costlessly observable

• then worker has the incentive to shirk

One Possible Solution

• Let the worker buy the right to all of their output

• Worker pays the firm 1,500 for the right to all of the gross benefits

• Will the worker behave efficiently?

Problem with Ownership

• Wealth constraint - labor may not have the resources to become franchisee

• Risk aversion - output is a function of more than just effort

• Team production - benefits are an inseparable function of effort made by many different workers

Piece Rate Contract

• Pays a fee for each unit of output

• This provides incentives for worker to work

• possibly producing too much

Second Best Contract

• Compensation as a function of performance• W = a + BX

• B increases with– ability of the agent to bear risk– lower effort costs by the agent– higher marginal contribution of effort– clear performance measure

Math Example

• Suppose “e” cannot be observed but gross revenue can be

• Suppose gross revenue depends on worker’s effort plus other factors

Revenue = f(e, X)

B =5000 B = 4000

e = 50 Prob=3/4 Prob=1/4

e = 40 Prob=1/4 Prob=3/4

Incentive Compatibility

• Establish a salary structure so that workers

• U(e =50) > U(e=40)

Incentive Compatibility

• Establish a salary structure so that workers

• U(e =50) > U(e=40)

• Ex: Let Y = salary when B = 5000

• and let Z = salary when B = 4000

• Then Incentive compatibility requires

• 3/4(Y-2500) + 1/4(Z-2500) > 1/4(Y-1600) + 3/4(Z-1600)

Incentive Compatibility

• Incentive compatibility requires

• 3/4(Y-2500) + 1/4(Z-2500) > 1/4(Y-1600) + 3/4(Z-1600)

• Solving yields Y > Z + 1800

• What happens when the riskiness of those revenues falls?

• What happens when the riskiness of those revenues falls?

• You reduce the premium paid for the higher productivity

Other Shirking Deterrents

• Bonding

Other Shirking Deterrents

• Bonding

• Back-loading

Other Shirking Deterrents

• Bonding

• Back-loading

• Bonuses

Other Shirking Deterrents

• Bonding

• Back-loading

• Bonuses

• Promotions