Smeal College of Business Managerial Accounting: B A 521Pennsylvania State University Professor HuddartGSB, Inc.: Transfer Prices and Resource AllocationGrapple Synthetics of Boonton (GSB), Inc., has a problem concerningits computer facilities. Its computer facility services 600 identical users withtwo 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 firstcomputer and the total number of users of that computer is n, the individualuser 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 ofusers of that computer is m, the user increases her daily productivity by theamount $(10 − m/30). These relationships are captured in the tables below.Assume throughout that these 600 users are all there are; no new ones willappear. The marginal cost of servicing a user is zero. And don’t worry ifyour 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, choosingso as to maximize her individual productivity gain from the computerunder the assumption that other users will stick with the computers theyhave chosen. Assuming that this is so, what is the equilibrium allocationof users to the two computers? How many are using computer 1; howmany 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 maxi-mizing the total contribution possible for GSB. He suggests the followingscheme of transfer prices: A “price per day” will be named for the ser-vices of the computers, and users should be told to make use of eithercomputer only if the productivity gain they attain in so doing exceedsthis “transfer price.” What (single) price per day should GSB name,assuming that its computer users will honestly allocate themselves be-tween computers (or no use) to maximize individual productivity gainModified 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/sjh11B A 521 GSB, Inc.less transfer price? What will be the resulting usage for the two com-puters? [Hint: If you have trouble getting started, try to discover whatwould happen if the single price of $5 per day were charged (for eachcomputer).](c) The head of the accounting department at GSB thinks that this transferprice scheme is a good idea, but she suggests a more complex schemein which a different price per day will be charged for each of the twocomputers. What is the optimal scheme of this sort? What is theresulting pattern of usage for the two computers?(d) The head of the economic analysis department at GSB is quite confusedby the answers you obtained in parts (b) and (c). He says that he recallsfrom his old days as a microeconomist something called the secondtheorem of welfare economics, in which it was claimed that efficientallocations of resources should follow the dictates of a (Walrasian)market mechanism. He points out that if the computer services wereserved by competitive outside vendors (that is, users would actuallypay a market price for the services they used), then the competitiveprice would equal marginal cost, which is zero. Thus zero transfer priceshould lead to an efficient solution. He suggests that you recheck youralgebra in part (b) and (c). In no more than 200 words, explain to thisindividual why he should, instead, check his economics textbook.Benefit to user of working on a computerNumber of Computer 1 Computer 2Users (30 − n/10) (10 − m/30)90 21.00 7.00150 15.00 5.00225 7.50 2.50300 0.00 0.00Page 2GSB, Inc. B A 521Number of UsersTransfer Computer 1 Computer 2Price n = 300 − 10t m = 300 − 30t0.00 300 3002.50 275 2255.00 250 1507.50 225 7510.00 200 012.50 175 015.00 150 017.50 125 020.00 100 0Page