ajaz_eco204_2009_HW_13

ajaz_eco204_2009_HW_13 - University of Toronto, Department...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain HW 13 Please help improve the course by sending me an email about typos or suggestions for improvements _____________________________________________________________________________________ Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 Founded in October 2009 by former ECO 204 students 1 , the aptly titled The Not So Prestigious Data Services Company (TNSPDS) has never been profitable. The company provides ECO 204 HW solutions to lazy bones, sorry, customers, who pay an hourly fee access to solutions on TNSPDS servers and discuss these with live agents. The company has also signed an annual contract with Ecowoman (a tutoring service) for an average of 90 hours a month billed at $400/hour (Ecowoman uses the services to download solutions). All other "commercial" customers are billed $500/hour. Exhibit 1 contains a breakdown of contractual and commercial hours and Exhibit 2 breaks down revenues. The company has to service its servers for about 30 hours a month (i.e. an hour a day) please see Exhibit 1. The Not So Prestigious Date Services Company has signed several multiyear contracts for servers, space (a room in Goodsworth College) and custodial services. Some operations staff is salaried while systems maintenance, administration and sales staff are wholly salaried. The company spends $30,000/month promoting its services (see for example this Facebook group). See Exhibit 2 for detailed cost information. The Not So Prestigious Date Services Company hired the Bad Consulting Group (BCG) to estimate the cost function. BCG consultants recognized that power and operations costs are quasivariable and quasifixed. They estimated the power cost function by fitting a linear trend 1 Dr. Sloth, Miss Yawn, Miss Miss Klass and Mr. Sans Case 1 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain line in a scatter plot of power expenses vs. revenue plus service hours (since power is consumed during maintenance): The BCG consultants estimated the operations cost function by fitting a 2nd order polynomial trend line in a scatter plot of operations expenses vs. revenue hours: Note: Here, the "best fitting line" is linear for power cost and nonlinear for operations. In ECO 220 you will see how to determine the "best fitting" functional form (i.e linear vs. nonlinear). 2 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain Based on BCG's analysis and denoting hours by : Power Cost Operations Cost 100 4 600 500 2 2 0.1667 0.1667 Power Cost Operations Cost Adding the fixed cost of power and operations ($600) to all other fixed costs ($100,000) yields the total fixed cost 100,600 so that the total cost function is: 100,600 2 0.1667 Observe that 2 0.1667 is a convex function from which we can deduce that the company has decreasing returns with respect to the variable inputs (quasivariable cost and quasivariable operations). Exhibits 1 and 2 are in the Appendix. (a) Some managers think that raising commercial prices by $100/hour in December 2009 will lead to a 25% decrease in commercial hours and lowering commercial prices by $50/hour in December 2009 will lead to a 12.5% increase in commercial hours. What is the demand equation of commercial customers in December 2009? Hint: You did a similar exercise in HW 1 and hopefully in paper 1. (b) Solve for the profit maximizing (or loss minimizing) commercial hours in December 2009 by assuming there is no capacity constraint. Hint: Since Ecowoman has signed a contract, E is a constant. As such, you can treat the commercial side of the business as an independent entity and solve the profit maximization problem: max C 2 0.1667 is the total fixed cost of the commercial side of the business. (c) Solve for the profit maximizing (or loss minimizing) commercial hours in December 2009 by recognizing there is a capacity constraint. Hint: Since Ecowoman has signed a contract, E is a constant. As such, you can treat the commercial side of the business as an independent entity. Moreover, of the total hours in December 2009, 90 hours are allocated to Ecowoman and 31 hours are for service so that commercial hours must be less than or equal to 309. Now solve this problem using the KuhnTucker technique: max C 2 0.1667 . . 309 is the total fixed cost of the commercial side of the business. 3 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain (d) Solve for the profit maximizing (or loss minimizing) commercial hours in December 2009 by assuming there are 2 available hours: Exhibit 1 Not so Prestigious Data: Summary of Server Utilization, Fourth Quarter 2009 Revenue Hours October November December Contract Commercial Total revenue hours Service hours Available hours Total hours 90 90 180 31 490 701 90 125 215 30 389 634 90 120 210 31 2 243 Hint: Since Ecowoman has signed a contract, E is a constant. As such, you can treat the commercial side of the business as an independent entity. Moreover, of the total hours in December 2009, 90 hours are allocated to Ecowoman and 31 hours are for service so that commercial hours must be less than or equal to 122. Now solve this problem using the Kuhn Tucker technique: max C 2 0.1667 . . 122 is the total fixed cost of the commercial side of the business. 4 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain APPENDIX Exhibit 1 Not so Prestigious Data: Summary of Server Utilization, Fourth Quarter 2009 Revenue Hours October November December Contract Commercial Total revenue hours Service hours Available hours Total hours 90 90 180 31 490 701 90 125 215 30 389 634 90 120 210 31 189 430 5 University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain Exhibit 2 Not so Prestigious Data Services Summary Results of Operations, Fourth Quarter 2009 October Revenues Contract Revenue Commercial Revenue Total Revenue Expenses Space costs Rent Custodial services Total Equipment costs Server leases Maintenance Depreciation: Server Equip. Office Equip. Power Total Wages and salaries Operations Systems maintenance Administration Sales Total Sales promotions 20,000.00 20,000.00 20,000.00 1,000.00 1,000.00 1,000.00 21,000.00 21,000.00 21,000.00 36,000.00 36,000.00 36,000.00 45,000.00 62,500.00 60,000.00 81,000.00 98,500.00 96,000.00 November December 10,000.00 10,000.00 10,000.00 1,000.00 1,000.00 1,000.00 300.00 300.00 300.00 200.00 200.00 200.00 944.00 1080 1,064.00 12,444.00 12,580.00 12,564.00 5,541.08 10,000.00 15,000.00 12,500.00 43,041.08 7,775.71 10,000.00 15,000.00 12,500.00 45,275.71 7,431.47 10,000.00 15,000.00 12,500.00 44,931.47 30,000.00 30,000.00 30,000.00 Total expenses 106,485.08 108,855.71 108,495.47 Net Income (25,485.08) (10,355.71) (12,495.47) 6 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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