Smeal College of Business Pennsylvania State University Managerial Accounting B A 521 Professor Huddart GSB Inc Transfer Prices and Resource Allocation Grapple Synthetics of Boonton GSB Inc has a problem concerning its computer facilities Its computer facility services 600 identical users with two computers one of which has a bit more software support than the other but is more liable to congestion Specifically if one of the users uses the first computer and the total number of users of that computer is n the individual user is able to increase her daily productivity by an amount 30 n 10 And if one of the users uses the second computer and the total number of users of that computer is m the user increases her daily productivity by the amount 10 m 30 These relationships are captured in the tables below Assume throughout that these 600 users are all there are no new ones will appear The marginal cost of servicing a user is zero And don t worry if your answers don t come out in even integers fractional users will be okay for purposes of this problem a Until now GSB has not tried at all to regulate use of its computers Each user has allocated herself to one of the two computers choosing so as to maximize her individual productivity gain from the computer under the assumption that other users will stick with the computers they have chosen Assuming that this is so what is the equilibrium allocation of users to the two computers How many are using computer 1 how many are using computer 2 and how many are using neither b The head of the computer center at GSB is concerned that the current unregulated method of allocating individuals to computers is not maximizing the total contribution possible for GSB He suggests the following scheme of transfer prices A price per day will be named for the services of the computers and users should be told to make use of either computer only if the productivity gain they attain in so doing exceeds this transfer price What single price per day should GSB name assuming that its computer users will honestly allocate themselves between computers or no use to maximize individual productivity gain Modified from David M Kreps 1990 A Course in Microeconomic Theory Princeton N J Princeton University Press c Steven Huddart 1995 2009 All rights reserved www personal psu edu sjh11 B A 521 GSB Inc less transfer price What will be the resulting usage for the two computers Hint If you have trouble getting started try to discover what would happen if the single price of 5 per day were charged for each computer c The head of the accounting department at GSB thinks that this transfer price scheme is a good idea but she suggests a more complex scheme in which a different price per day will be charged for each of the two computers What is the optimal scheme of this sort What is the resulting pattern of usage for the two computers d The head of the economic analysis department at GSB is quite confused by the answers you obtained in parts b and c He says that he recalls from his old days as a microeconomist something called the second theorem of welfare economics in which it was claimed that efficient allocations of resources should follow the dictates of a Walrasian market mechanism He points out that if the computer services were served by competitive outside vendors that is users would actually pay a market price for the services they used then the competitive price would equal marginal cost which is zero Thus zero transfer price should lead to an efficient solution He suggests that you recheck your algebra in part b and c In no more than 200 words explain to this individual why he should instead check his economics textbook Number of Users 90 150 225 300 Benefit to user of working on a computer Computer 1 Computer 2 30 n 10 10 m 30 21 00 15 00 7 50 0 00 Page 2 7 00 5 00 2 50 0 00 GSB Inc B A 521 Transfer Price 0 00 2 50 5 00 7 50 10 00 12 50 15 00 17 50 20 00 Number of Users Computer 1 Computer 2 n 300 10t m 300 30t 300 275 250 225 200 175 150 125 100 Page 3 300 225 150 75 0 0 0 0 0