Question

Three firms can supply a college with some application software. Each firm has a different pricing structure: the first firm provides a site license which costs $130,000 and can be used by anyone at the college. The second firm charges $1000 per user and the third charges a fixed amount of $40,000 for the first 60 users and $500 for each additional user.

1. Draw a graph of each cost function on the same set of axes.
2. What advice can you give the college about which company to use?

Answer 1

Each of the three firms offers a different cost structure. The costs for the college can be broken down into variable and fixed costs.

• Firm 1 has a fixed cost of $130,000 and no variable costs
• Firm 2 has no fixed costs, but variable costs of $1000 per user
• Firm 3 has a fixed cost of $40,000 for the first 60 users, and $500 for every extra user after 60

---

Thus, for the college,

C1 = 130,000

C2 = 1000x

C3 = 40000 + 500y (where y = the number of students above x = 60)

where, C is the cost to the college, and x is the number of users

---

Graphically, the three cost functions are as under:

---

If the college has a very large number of students, any number greater than or equal to 240, they should select Firm 1.

If the college has a small number of students, any number less than or equal to 40, they should select Firm 2 or Firm 3. Both will have the same cost.

If the college has more than 40 students but less than 240, they should select Firm 3.

---

Firm 1 is ideal for a very large college, as it gives unlimited access for $130,000.

Firm 2 is ideal for a small college of 40 students or less, as it has a per student cost only.

Firm 3 is ideal for a mid-sized college, between 40 and 240 students. It also offers flexibility, if the number of students above 60. However, if the number is more than 240, it is too costly.