ch 14 agency. principal-agent relationship principal owns an asset agent works on principal’s...
TRANSCRIPT
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Ch 14 Agency
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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
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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
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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
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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
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Who is to be the monitor?
• The party with the least incentive to shirk
• The least mobile party
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Who is to be the monitor?
• For efficiency- the party central to all contracts
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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
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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
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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
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Math Example
• Thus, the cost to the firm is:
• C = 1000 + e2
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Math example
• Suppose the firm benefits by $100 for each extra unit of effort made by the employee
• B = 100e
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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
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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
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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
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Problem
• If the salary is fixed at $3,500 and “e” is not costlessly observable
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Problem
• If the salary is fixed at $3,500 and “e” is not costlessly observable
• then worker has the incentive to shirk
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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?
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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
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Piece Rate Contract
• Pays a fee for each unit of output
• This provides incentives for worker to work
• possibly producing too much
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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
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Math Example
• Suppose “e” cannot be observed but gross revenue can be
• Suppose gross revenue depends on worker’s effort plus other factors
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Revenue = f(e, X)
B =5000 B = 4000
e = 50 Prob=3/4 Prob=1/4
e = 40 Prob=1/4 Prob=3/4
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Incentive Compatibility
• Establish a salary structure so that workers
• U(e =50) > U(e=40)
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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)
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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
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• What happens when the riskiness of those revenues falls?
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• What happens when the riskiness of those revenues falls?
• You reduce the premium paid for the higher productivity
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Other Shirking Deterrents
• Bonding
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Other Shirking Deterrents
• Bonding
• Back-loading
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Other Shirking Deterrents
• Bonding
• Back-loading
• Bonuses
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Other Shirking Deterrents
• Bonding
• Back-loading
• Bonuses
• Promotions