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 - e 2 ) Worker requires a minimum $1,000 just to show up for work

Math Example Workers utility function U = (I - e 2 ) 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 = e 2

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 - ( e 2 ) dProfit/de = e Set equal to zero, yields e =50

Profit Maximization By paying the worker = $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)

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

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