UNIVERSITY OF TORONTO Faculty of Arts and Sciences August Examinations 2011 ECO 204 Y1Y. Please give your name and ID # as it appears in ROSI

Transcription

1 UNIVERSITY OF TORONTO Faculty of Arts and Sciences August Examinations 2011 ECO 204 Y1Y Duration: 3 hours Total Points: 150 points Examination Aids Allowed: Calculator. Instructions: - This exam consists of 6 questions in 36 pages, double-sided. Please give your name and ID # as it appears in ROSI Last Name: First Name: Student ID # Question Points Scores Total score (out of 150 points) / 150 YOU MUST STAY SEATED DURING THE LAST 10 MINUTES OF THE FINAL EXAM WAIT UNTIL ALL EXAMS ARE COLLECTED FOR YOUR CONVENIENCE, THERE ARE TWO WORKSHEETS AT THE END OF THIS EXAM KEEP ANSWERS BRIEF TO EARN CREDIT, SHOW CALCULATIONS AND GIVE ARGUMENTS TO SUPPORT YOUR ANSWERS Good luck! Page 1 of 36

2 FORMULAS ( ) are random variables and are constants In a portfolio of two risky assets A and B with fraction ( ) in risky asset A: ( [ ] ) ( [ ] ) ( [ ] ) ( [ ] ) ( [ ] ) [ [ ] [ ] ] Page 2 of 36

3 QUESTION 1 [10/150 POINTS] The following table contains revenues (in dollars) for each of the 25 firms in the US pharmacy benefit manager (PBM) industry (as of July 21 st, 2011) 1 : Firm Name Revenues ($) 1 Express Scripts, Inc. 90,000,000 2 CVS/Caremark Rx, Inc. 85,100,000 3 Medco Health Solutions, Inc. 65,000,000 4 ICORE Healthcare, Inc. 60,000,000 5 Health Information Designs, Inc. 52,000,000 6 NovoLogix 40,000,000 7 MedImpact Healthcare Systems, Inc. 32,000,000 8 Argus Health Systems, Inc. 28,600,000 9 HealthTrans 15,100, Prime Therapeutics LLC 15,000, Provider Synergies, LLC 14,000, ACS, Inc. 14,000, Prescription Solutions 12,204, RxStrategies, Inc. 12,000, RESTAT, LLC 12,000, ScriptSave 12,000, Aetna Pharmacy Management (APM) 11,000, First Health Services Corporation 10,000, Walgreens Health Services Division 9,700, Acro Pharmaceutical Services 7,000, CIGNA Pharmacy Management 6,500, Catalyst Rx 6,482, Axium Healthcare Pharmacy, Inc. 6,000, SXC Health Solutions, Inc./InformedRx 5,500, Sanovia Corporation 5,000,000 TOTAL MARKET REVENUE 626,187,684 1 Source: Page 3 of 36

4 (1) [5 points] According to the measure of market structure, is the PBM industry effectively competitive, oligopolistic, or effectively monopolistic? State all assumptions and show all calculations. Page 4 of 36

5 (2) [5 points] Recently, Express Scripts and Medco proposed a horizontal merger. According to based guidelines for mergers, should this merger be blocked? State all assumptions and show all calculations. Page 5 of 36

6 QUESTION 2 [15/150 POINTS] (1) [5 points] Suppose two separate companies own two separate hydro-electric dams on the same river. For example, company A owns a dam upstream while company B owns a dam downstream. Are there economies of scope from a merger of these two companies (i.e. now operating as one company with two dams)? Give a brief explanation. Page 6 of 36

7 (2) [5 points] Over the past few years many beer breweries have merged with US but not French wineries. Give a brief explanation for why there are economies of scope in mergers between beer breweries and US wineries but not between beer breweries and French wineries. Give a brief explanation. Page 7 of 36

8 (3) [5 points] Which of the following cost functions exhibit economies of scope? ( ) ( ) ( ) State all assumptions and show all calculations. Hint: What is the definition of economies of scope? Page 8 of 36

9 QUESTION 3 [35/150 POINTS] The following table contains figures for Apple s ipod price per unit, 000s of units sold, and the gross margin to revenue ratio from 2007 through 2010: Apple ipod Prices, Units Sold and Gross Margin to Revenue Ratio Year Price per ipod, '000s of units sold, Gross Margin to Revenue Ratio 2007 $161 51, $164 54, $149 54, $167 50, Source: Apple Annual Reports (1) [5 points] What is the of an ipod in each year from 2007 through 2010? State all assumptions and show all calculations. Page 9 of 36

10 (2) [5 points] In which year was demand for ipods most and least price sensitive? Hint: Compute elasticities to 4 decimal places. State all assumptions and show all calculations. Page 10 of 36

11 (3) [5 points] Using Excel, the demand function for Apple ipods over was estimated to be: What is the total market size for Apple ipods? What is the maximum price customers are willing to pay for an ipod? State all assumptions and show all calculations. Page 11 of 36

12 (4) [10 points] Suppose Apple s goal is to choose output of ipods ( 000s) to maximize total revenues: Here 000s of units and capacity. Setup this optimization problem in parametric form and (only) derive the condition for when Apple should not sell ipods (i.e. not serve the market). Assume the demand function is where. State all assumptions and show all calculations. Page 12 of 36

13 Page 13 of 36

14 (5) [10 points] Suppose Apple s goal is to choose output of ipods ( 000s) to maximize total profits: Here 000s of units and capacity. Setup this optimization problem parametric form and (only) derive the condition for when Apple should not sell ipods (i.e. not serve the market). Assume the demand function is where and use the ( ) from State all assumptions and show all calculations. Page 14 of 36

15 Page 15 of 36

16 QUESTION 4 [5/150 POINTS] Prove that a competitive firm with increasing returns cannot maximize profits. Assume capacity. State all assumptions and show all calculations. and that Page 16 of 36

17 QUESTION 5 [40/150 POINTS] A company produces output using capital labor, and materials as complementary inputs. Each unit of capital must be paired with 2 workers and each unit of capital must be paired with a unit of materials. Assume all inputs are variable, denote the company s state of technological progress/management by, target output by, and price of labor, capital and materials by respectively. Assume. (1) [5 points] Assume the company leases capital. Derive the company s cost function, i.e. ( ). State all assumptions and show all calculations. Page 17 of 36

18 (2) [5 points] Characterize this company s returns to scale, i.e. does it have increasing, constant, or decreasing returns to scale? State all assumptions and show all calculations. Page 18 of 36

19 (3) [5 points] What is the minimum efficient scale ( )? State all assumptions and show all calculations. Page 19 of 36

20 (4) [5 points] What is the elasticity of total cost ( ) with respect to target output? State all assumptions and show all calculations. Page 20 of 36

21 Now assume that instead of leasing capital, the company owns capital to produce output. The company purchased capital at the purchase price of the capital was ( ) and capital has a lifetime of periods. Denote the opportunity cost rate of return in period by ( ). (5) [5 points] Suppose this company uses straight line deprecation methods. What is, the depreciation of capital, in each period? State all assumptions and show all calculations. : Page 21 of 36

22 (6) [5 points] Derive an expression for ( ), the value of capital in period, in terms of ( ) ( ) and only. State all assumptions and show all calculations. Page 22 of 36

23 (7) [5 points] Derive an expression for ( ), the user cost of capital in period, in terms of ( ) ( ) and only. State all assumptions and show all calculations. Page 23 of 36

24 (8) [5 points] The price of (owned) capital ( ) falls over time : True or false? State all assumptions and show all calculations. Page 24 of 36

25 QUESTION 6 [45/150 POINTS] (1) [5 points] What is a risky asset? What is a risk free asset? In particular, are 10 year Canadian government bonds risk free? Give a brief explanation. Page 25 of 36

26 (2) [5 points] Below is a histogram and descriptive statistics of monthly returns on US 30-day T-Bills from Dec 31 st 1925 to Dec 31 st Are 30 day US T-Bills risk free? Give a brief explanation. Average (Monthly) Return Variance of (Monthly) Returns Standard Deviation of (Monthly) Returns Page 26 of 36

27 (3) [5 points] The following table contains Shell Oil Company s monthly closing price, monthly returns, and monthly returns without dividends over July 2010 December 2010: Shell Oil Company Date Price Return Return without Dividend 7/30/ /31/ /30/ /29/ /30/ /31/ What was the dividend in August 2010, November 2010, and December 2010? State all assumptions and show all calculations. Page 27 of 36

28 (4) [10 points] The following table contains the return on US 30 day T-Bills purchased on Dec 31 st 2010 and the average and variance of Shell Oil Company s monthly returns (August 2005 to December 2010): 30 Day US T-Bill Return (issued Dec 31 st 2010) Shell Oil Average Monthly Return Shell Oil Variance of Monthly Return Consider an investor with a mean-variance utility function. What is the parameter of risk intolerance if she borrows 10% of her funds to invest in a portfolio of 30-day US T-Bills and Shell Oil stocks in December 2010? State all assumptions and show all calculations. Page 28 of 36

29 Page 29 of 36

30 (5) [10 points] The following table contains the average, variance, and covariance of Shell Oil Company s and Research in Motion s (RIM) monthly returns (August 2005 to December 2010) Shell Oil Average Monthly Return Shell Oil Variance of Monthly Return RIM Average Monthly Return RIM Variance of Monthly Return Covariance Shell Oil and RIM Monthly Return Suppose an investor allocates funds between Shell Oil and RIM stocks. What fraction of this portfolio consists of RIM stocks if her goal is to minimize portfolio risk? State all assumptions and show all calculations. Page 30 of 36

31 Page 31 of 36

32 (6) [10 points] The following table contains the return on 30 day US T-Bills purchased on Dec 31 st 2010 as well as the average, variance, and covariance of Shell Oil Company s and Research in Motion s (RIM) monthly returns (August 2005 to December 2010) 30 Day US T-Bill Return (Dec 31st 2010) Shell Oil Average Monthly Return Shell Oil Variance of Monthly Return RIM Average Monthly Return RIM Variance of Monthly Return Covariance Shell Oil and RIM Monthly Return Consider an investor with a mean-variance utility function. What is the parameter of risk intolerance if she borrows 10% of her funds to invest in a portfolio of 30-day US T-Bills and a composite risky asset consisting of Shell Oil and RIM stocks in December 2010? State all assumptions and show all calculations. Page 32 of 36

33 Page 33 of 36

34 Page 34 of 36

35 WORKSHEET Page 35 of 36

36 WORKSHEET Page 36 of 36