Question

Three companie are bidding to sell statistical software for an Econ Department. Assume the software that each company is offering to sell is of equal quality.

Company A offers the software license for $260,000

Company B charges $2,000 per user

Company C charges a fixed cost of $80,000 for the first 60 users and $1,000 for each additional user.

Assume Users (U) on x-axis and Costs (C) on the y-axis.

a.) Write out the cost equation for companies A, B. and C.

b.) On one graph, draw each of the cost functions for companies A, B, and C.

c.) What advice will you give the Econ when it comes to making a decision on which company to purchase software from.

Answer 1

a)

Company A offers the license for a fixed cost of $260,000. The cost function for A is C= 260,000

Company B offers the license for a variable cost of $2000 per user. The cost function for B is C= 2000 U

Company C offers the license for a fixed cost of $80000 for first 60 users and a variable cost of $1000 per user beyond 60 users. The cost function for C is C= 80000 + 1000 (61 + U)

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b)

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c) The department will choose the company that offers the least cost for the software license. The decision will depend on the number of users the department has. For example, if the department has a large number of users, above 180 then the best option is to choose comapny A because the cost charged by company C for 180 users will be $260000 and $360000 by Company B. The department thus will be indifferent between choosing company A and C. However, any less number of users the company A offers the maximum costs.

Number of users	Company A offers	Company B offers	Company C offers	Decision
<=40	260000	<=80000	80000	Company B
40<U<60	260000	80000 < C < 120000	80000	Company C
80	260000	160000	160000	Company B or C
81<U < 179	260000	2000*U (Always more than what company C charges 162000 < C < 358000	80000 + 1000 (61+U) = 161000 < C <259000	Company C
180	260000	360000	260000	Company A or C
> 180	260000	> 360000	> 260000	Company A

Hence, it depends on the number of users (more than 180) the department has. The more the users, purchasing license from company A is preferred since no variable cost has to be given. However, the deicision should ideally be based on whether the department has been able to cover its variable costs. Hence, it is suggested that the department should consider buying from company B in case of less than 40 users and from C in case of number of users between 40 and 60 users.

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