Consider a firm wishing to use the services of a consultant. The marginal benefit for the firm is given by MB = 120 – q, where q is the quantity of services provided. The marginal cost of those services for the consultant is given by MC = 2q. The issue for the parties is that it is difficult to verify the actual quantity of consulting services provided. To help mitigate this the firm can hire an auditor at a cost of $100. Similarly, the consultant can use some recording keeping techniques that cost $200. Even with both of these actions, if the consultant provides less than 60 units of the service it will look like zero quantity was provided to a third party (like a court enforcing the contract). What is the total agency cost in this case? Using the help of a diagram, explain your answer. What if the auditing service instead cost the firm $1000 and the record keeping technology cost the consultant $1000 – what would the total agency cost be in this case? Explain your answer
Question
Consider a firm wishing to use the services of a consultant. The marginal benefit for the firm is given by MB = 120 – q, where q is the quantity of services provided. The marginal cost of those services for the consultant is given by MC = 2q. The issue for the parties is that it is difficult to verify the actual quantity of consulting services provided. To help mitigate this the firm can hire an auditor at a cost of 200. Even with both of these actions, if the consultant provides less than 60 units of the service it will look like zero quantity was provided to a third party (like a court enforcing the contract). What is the total agency cost in this case? Using the help of a diagram, explain your answer. What if the auditing service instead cost the firm 1000 – what would the total agency cost be in this case? Explain your answer
Solution
The agency cost in this case is the cost incurred due to the principal-agent problem, where the principal (the firm) and the agent (the consultant) have different interests and asymmetric information.
First, let's find the quantity of services that maximizes the net benefit for the firm. This is where the marginal benefit equals the marginal cost, i.e., 120 - q = 2q. Solving this equation gives q = 40.
However, due to the verification problem, if the consultant provides less than 60 units of service, it will look like zero quantity was provided. Therefore, the firm has to hire an auditor at a cost of 200.
So, the total agency cost in this case is the cost of the auditor plus the cost of record keeping, plus the loss in net benefit due to the consultant providing 60 units of service instead of the optimal 40 units. This is 200 + (60 - 40) * 2 = $500.
If the auditing service instead cost the firm 1000, the total agency cost would be 1000 + (60 - 40) * 2 = $2440.
This shows that the agency cost can be significantly higher when the costs of monitoring and enforcing the contract are high. This is a common problem in principal-agent relationships, and it's one of the reasons why firms often prefer to hire employees rather than independent contractors for certain tasks.
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