The local operations manager for the Canada Revenue Agency decides whether to hire one,two,or three temporary tax examiners for the upcoming tax season.She estimates that net revenues (in thousands of dollars)will vary with how well taxpayers comply with the new tax code just passed by Parliament,as follows: If she feels the chances of low,medium,and high compliance are 20%,30%,and 50%,respectively,what is her expected value of perfect information?

Question

The local operations manager for the Canada Revenue Agency decides whether to hire one,two,or three temporary tax examiners for the upcoming tax season.She estimates that net revenues (in thousands of dollars)will vary with how well taxpayers comply with the new tax code just passed by Parliament,as follows:  If she feels the chances of low,medium,and high compliance are 20%,30%,and 50%,respectively,what is her expected value of perfect information?

Quizplus · Accepted Answer

To determine the expected value of perfect information, we need to compare the expected values with and without perfect information.

Without perfect information:

- If she hires one tax examiner and compliance is low, net revenue is $5,000. 
- If she hires one tax examiner and compliance is medium, net revenue is $20,000. 
- If she hires one tax examiner and compliance is high, net revenue is $35,000. 
- If she hires two tax examiners and compliance is low, net revenue is $10,000. 
- If she hires two tax examiners and compliance is medium, net revenue is $30,000. 
- If she hires two tax examiners and compliance is high, net revenue is $50,000. 
- If she hires three tax examiners and compliance is low, net revenue is $15,000. 
- If she hires three tax examiners and compliance is medium, net revenue is $40,000. 
- If she hires three tax examiners and compliance is high, net revenue is $60,000.

Now we calculate the expected value without perfect information as follows:

E(net revenue without perfect info) = (0.2 x 5) + (0.3 x 20) + (0.5 x 35) + (0.2 x 10) + (0.3 x 30) + (0.5 x 50) + (0.2 x 15) + (0.3 x 40) + (0.5 x 60)

E(net revenue without perfect info) = $32,500

With perfect information, she can make the best hiring decision based on the compliance level. Therefore, the expected value with perfect information is the same as the maximum net revenue for each compliance level:

E(net revenue with perfect info) = (0.2 x 15) + (0.3 x 40) + (0.5 x 60)

E(net revenue with perfect info) = $43,500

The expected value of perfect information is the difference between the two:

EVI = E(net revenue with perfect info) – E(net revenue without perfect info)

EVI = $43,500 – $32,500

EVI = $11,000

Therefore, the best choice is to hire three tax examiners if the estimated compliance is high (50% chance), as this would result in the maximum expected net revenue of $60,000.

The Local Operations Manager for the Canada Revenue Agency Decides