Please Write Your Name and ID # (as these appear in ROSI) Last Name: First Name: ID #

Transcription

1 UNIVERSITY OF TORONTO Faculty of Arts and Sciences August Examinations 2012 ECO 204 Y1Y Duration: 3 hours Total Points: 100 points Examination Aid Allowed: Calculator. Instructions: - This exam consists of 6 questions in 29 pages, double-sided. Please Write Your Name and ID # (as these appear in ROSI) Last Name: First Name: ID # YOU CANNOT LEAVE THE EXAM ROOM DURING THE LAST 10 MINUTES PLEASE REMAIN SEATED UNTIL THE PROCTOR ANNOUNCES THAT YOU CAN LEAVE THE ROOM. IF YOU DETACH ANY PAGES THEN IT S YOUR RESPONSIBILITY TO RE-STAPLE THE PAGES KEEP ANSWERS AS BRIEF AS POSSIBLE THERE ARE 2 WORKSHEETS AT THE END OF THIS EXAM Graders: Please Input Scores Below Question Maximum Possible Points Score Question 1 15 Question 2 15 Question 3 20 Question 4 15 Question 5 20 Question 6 15 Total Points = 100 Final Exam Checked by Instructor? Yes No Page 1 of 29

2 ALL QUESTIONS IN THIS FINAL EXAM ARE BASED ON THE FOLLOWING INFORMATION ABOUT AMD AND INTEL The economist, Hugo Salgado, estimated the following demand models for Intel and AMD PC (personal computer) CPU chips (Central Processing Units): The subscripts and refer to AMD and Intel respectively where CPU and quantity of CPUs (millions). Notice these demand models are of the form ( ) and ( ) respectively. Hugo also estimated AMD and Intel s average variable cost 1 : Throughout this final exam assume that AMD and Intel: are in the short run have ample capacity and will always produce strictly positive output (i.e. ). ALL QUESTIONS MUST BE ANSWERED SEQUENTIALLY ANSWERS TO STARRED * QUESTIONS WILL BE NEEDED TO ANSWER OTHER QUESTIONS. IF YOU GET STUCK ON A QUESTION THAT DOES NOT HAVE A STAR * THEN YOU SHOULD MOVE ON AND COME BACK LATER PLEASE CALCULATE ALL ANSWERS TO 3 DECIMAL PLACES 1 The cost figures used in this final exam are slightly different from the original estimates. For this final exam use,. Page 2 of 29

3 Question 1 [15 Points] * (1.1) [5 Points] What kind of returns to variable inputs do AMD and Intel have? Give a brief explanation. Page 3 of 29

4 * (1.2) [5 Points] Suppose AMD and Intel each have the following type of production function: Here output technology & management parameter fixed labor fixed capital variable materials are parameters. What is the numerical value of AMD s parameter? What is the numerical value of Intel s parameter? Hint: Both companies have the same value of. Show all calculations. Page 4 of 29

5 (1.3) [5 Points] Suppose AMD s production function is: where AMD s output AMD s technology & management parameter labor at AMD capital at AMD materials at AMD are parameters. Suppose Intel s production function is: where Intel s output Intel s technology & management parameter labor at Intel capital at Intel materials at Intel are parameters. Assume that AMD and Intel are currently: employing the same amount of labor (i.e. ) using the same level of capital (i.e. ) have identical parameters face identical input prices. True or false: AMD s technology and management is superior to Intel? Show all calculations and state all assumptions. Hint: Both Intel and AMD pay the same price for materials. Page 5 of 29

6 Question 2 [15 Points] * (2.1) [5 Points] Transform AMD s given demand model: ( ) into the demand model ( ). You will use this model later. Show all calculations. Page 6 of 29

7 * (2.2) [5 Points] Transform Intel s given demand model: ( ) into the demand model ( ). You will use this model later. Show all calculations. Page 7 of 29

8 * (2.3) [5 Points] Use your answers to parts (2.1) and (2.2) to derive the following two demand models for AMD and Intel respectively: ( ) ( ). You will use these models later. Show all calculations. Page 8 of 29

9 Page 9 of 29

10 Question 3 [20 Points] * (3.1) [5 Points] Use AMD s demand model from part (2.3) to answer this question. Suppose AMD is a monopolist -- calculate AMD s profit maximizing output and price. Show all calculations. Page 10 of 29

11 (3.2) [5 Points] What would be the impact on AMD s monopoly profits due to a hypothetical $1 increase in its marginal cost (in this question only)? Show all calculations. Page 11 of 29

12 * (3.3) [5 Points] Use Intel s demand model from part (2.3) to answer this question. Suppose Intel is a monopolist -- calculate Intel s profit maximizing output and price. Show all calculations. Page 12 of 29

13 (3.4) [5 Points] What would be the impact on Intel s monopoly profits due to a hypothetical $1 decrease in its marginal cost (in this question only)? Show all calculations. Page 13 of 29

14 * Question 4 [15 Points] Suppose AMD and Intel compete as Bertrand oligopoly rivals. Calculate each company s optimal output and price. Show all calculations. Page 14 of 29

15 Page 15 of 29

16 Question 5 [20 Points] * (5.1) [10 Points] Suppose AMD and Intel can charge either the monopoly price or the Bertrand oligopoly price. Please calculate and enter below the quantities, contribution margins, and gross margins (profits) for all four price combinations. Show all calculations and state all assumptions. AMD charges ENTER EACH COMPANY S CONTRIBUTION MARGIN FOR ALL 4 PRICE COMBINATIONS Monopoly Price Oligopoly Price Monopoly Price Intel charges Oligopoly Price AMD charges CALCULATE BELOW AND ENTER HERE EACH COMPANY S QUANTITY FOR ALL 4 PRICE COMBINATIONS Monopoly Price Oligopoly Price Monopoly Price Intel charges Oligopoly Price CALCULATE BELOW AND ENTER HERE EACH COMPANY S GROSS PROFITS FOR ALL 4 PRICE COMBINATIONS AMD charges Monopoly Price Oligopoly Price Monopoly Price Intel charges Oligopoly Price Below are the 4 set of calculations you need to do: Page 16 of 29

17 ❶ AMD charges monopoly price and Intel charges monopoly price ❷ AMD charges oligopoly price and Intel charges monopoly price Page 17 of 29

18 ❸ AMD charges monopoly price and Intel charges oligopoly price ❹ AMD charges oligopoly price and Intel charges oligopoly price Page 18 of 29

19 * (5.2) [5 Points] Suppose AMD and Intel play a one shot non-cooperative simultaneous move game in which each company can charge either the monopoly price or the Bertrand oligopoly price. Solve for the pure strategies Nash Equilibrium and indicate whether this is a prisoner s dilemma game. AMD charges ENTER EACH COMPANY S GROSS MARGIN (GROSS PROFITS) FOR ALL 4 PRICE COMBINATIONS AND SOLVE FOR THE PURE STRATEGY NASH EQUILIBRIUM Intel charges Monopoly Price Monopoly Price Oligopoly Price Oligopoly Price Page 19 of 29

20 (5.3) [5 Points] Please answer this question according to the last digit of your ID #: If your ID # ends in 0, 2, 4, 6, or 8 Suppose that AMD and Intel play the simultaneous move game in part (5.2) repeatedly forever. Suppose that in some period, AMD plays the cooperative price -- when will Intel cooperate with AMD? If required use where is the interest rate to discount cash flows. Show all calculations. If your ID # ends in 1, 3, 5, 7, or 9 Suppose that AMD and Intel play the simultaneous move game in part (5.2) repeatedly forever. Suppose that in some period, Intel plays the cooperative price -- when will AMD cooperate with Intel? If required use where is the interest rate to discount cash flows. Show all calculations. For your convenience you may wish to enter the gross margin figures from above: AMD charges ENTER EACH COMPANY S GROSS MARGIN (GROSS PROFITS) FOR ALL 4 PRICE COMBINATIONS Monopoly Price Oligopoly Price Monopoly Price Intel charges Oligopoly Price Page 20 of 29

21 Page 21 of 29

22 Question 6 [15 Points] (6.1) [5 Points] Please answer this question according to the last digit of your ID #: If your ID # ends in 0, 2, 4, 6, or 8 Assume AMD is a monopolist and is charging the profit maximizing price (calculated earlier) What is the AMD representative consumer s utility level of consuming AMD CPU chips? What is the AMD representative consumer s utility function (equation) of consuming AMD chips and everything else? Show all calculations and state all assumptions. If your ID # ends in 1, 3, 5, 7, or 9 Assume Intel is charging the profit maximizing price (calculated earlier) What is the Intel representative consumer s utility level of consuming Intel CPU chips? What is the Intel representative consumer s utility function (equation) of consuming Intel chips and everything else? Show all calculations and state all assumptions. Page 22 of 29

23 Page 23 of 29

24 (6.2) [5 Points] Please answer this question according to the last digit of your ID #: If your ID # ends in 0, 2, 4, 6, or 8 Use a consumer surplus argument to calculate the impact on the AMD representative consumer s total utility level due to a 1% excise tax on AMD chips. Show all calculations and state all assumptions. If your ID # ends in 1, 3, 5, 7, or 9? Use a consumer surplus argument to calculate the impact on Intel s representative consumer s total utility level due to a 1% excise tax on Intel chips. Show all calculations and state all assumptions. Page 24 of 29

25 Page 25 of 29

26 (6.3) [5 Points] Please answer this question according to the last digit of your ID #: If your ID # ends in 0, 2, 4, 6, or 8 Use a UMP argument to calculate the impact on the AMD representative consumer s total utility level due to a 1% income tax? Show all calculations and state all assumptions. If your ID # ends in 1, 3, 5, 7, or 9? Use a UMP argument to calculate the impact on the Intel representative consumer s total utility level due to a 1% income tax? Show all calculations and state all assumptions. Page 26 of 29

27 . Page 27 of 29

28 WORKSHEET Page 28 of 29

29 WORKSHEET Page 29 of 29