High School

There is one company that needs to hire an auditor for two years (this year and next year). Let's say that the incumbent auditor can perform the audit at a cost of $10. If the auditor is not an incumbent, the cost rises to $12 due to an extra $2 start-up cost (only the first time the auditor performs the audit).

In year 1, all auditors are non-incumbents with a cost of $12. If they set the price at $12, the company will randomly choose one. In year 2, the incumbent auditor will charge $10, while non-incumbents will charge $12. The company will continue with the incumbent auditor.

The incumbent can charge more than their cost since competition comes from non-incumbents. Non-incumbents may charge less than their costs to become the incumbent, as there is value to incumbency.

With a discount factor of 0.9, $1 next year is worth $0.9 today. If the value of being an incumbent next year is V, an auditor would be willing to charge their cost minus 0.9V this year, as they'll make the V back next year.

In year 2, one auditor will be the incumbent (the one who did the audit in year 1). The rest will be non-incumbents. Since there is no year 3, there is no value to incumbency at the end of year 2.

Questions:
1. What would be the price of a non-incumbent auditor in year 2?
2. What would be the price of the incumbent auditor in year 2?
3. How much profit will the incumbent auditor earn in year 2? (This answer determines the value of incumbency at the end of year 1.)
4. In year 1, what price will all auditors choose, considering there is no incumbent, but everyone desires the incumbency value calculated in part 1?
5. What is the profit of the auditor who becomes the incumbent in each of the two years? Calculate the present value of the profit as of year 1 using the formula: (year 1 profit) + 0.9 × (year 2 profit).

Answer :

In year 2, the price of a non-incumbent auditor will be $12, while the incumbent auditor will charge $10. The incumbent auditor will earn a profit of $10 in year 2.

In year 2, the non-incumbent auditors will continue to charge their cost of $12. This is because they do not have the advantage of incumbency and cannot charge more than their cost. The incumbent auditor, who performed the audit in year 1, will charge $10, which is their cost. They can charge less than non-incumbents because they have the advantage of incumbency.

The profit of the incumbent auditor in year 2 is $10. This is because the incumbent charges $10, which is their cost, and there are no startup costs in year 2. The incumbent auditor's profit is simply the price charged minus the cost.

In year 1, all auditors want to become the incumbent to obtain the value of incumbency in year 2. The price that all auditors will choose in year 1 depends on the value of incumbency. An auditor in year 1 would be willing to charge their cost minus 0.9V, where V represents the value of incumbency in year 2. Each auditor will try to set their price at a level that maximizes their chances of becoming the incumbent while still covering their costs.

To calculate the profit of the auditor who becomes the incumbent in each of the four years, we need more information. The given information only specifies the costs and prices for years 1 and 2. Without additional data, we cannot determine the profits or present value of profits beyond year 2.

To learn more about profit click here:

brainly.com/question/32381738

#SPJ11