University of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 2 GOOD LUCK! 9-DIGIT STUDENT ID # (AS IT APPEARS IN ROSI)

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1 University of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 2 TIME: 1 HOUR AND 50 MINUTES DO NOT HAVE A CELL PHONE ON YOUR DESK OR ON YOUR PERSON. ONLY AID ALLOWED: A CALCULATOR YOU CANNOT LEAVE THE EXAM ROOM DURING THE LAST 10 MINUTES OF THE TEST STAY SEATED UNTIL ALL TESTS HAVE BEEN COLLECTED AND THE PROCTORS ANNOUNCE THAT YOU CAN LEAVE THE ROOM IF YOU DETACH ANY PAGES FROM THE TEST, THEN YOU MUST RE-STAPLE THESE LOOSE PAGES TO THE TEST GOOD LUCK! LAST NAME (AS IT APPEARS IN ROSI): FIRST NAME (AS IT APPEARS IN ROSI): MIDDLE NAME (AS IT APPEARS IN ROSI) 9-DIGIT STUDENT ID # (AS IT APPEARS IN ROSI) SIGNATURE: DO NOT WRITE BELOW. FOR GRADER S USE ONLY Question Maximum Possible Points Score Total Points = 100 Page 1 of 15

2 Question 1 [45 POINTS] Ajax Airlines (AA) operates contractual and commercial cargo flights between Toronto and Montreal. Exhibit 1 contains the number of hours AA operated contractual and commercial cargo flights each month in 2013Q1. AA charges commercial customers $1,000/hour and under the terms of the contracted flights, the average monthly revenues are capped at $50,000. AA Contractual and Commercial Hours in 2013Q1 January 2013 February 2013 March 2013 April 2013 Contractual Hours/month Commercial Hours/month (a) [5 POINTS] Given that AA s average monthly contractual revenues are capped at $50,000 and calculate the uniform price ($/hour) AA charges its contractual customers. Show all calculations. Page 2 of 15

3 (b) [5 POINTS] In AA s management opinion, raising (lowering) the commercial price by 5% in April 2013 would ve decreased (increased) commercial monthly demand by 2.5%. Use these opinions to compute the price elasticity, commercial demand function, and the commercial demand curve. Justify the functional form (i.e. linear vs. non-linear) of the demand function/curve. Show all calculations. Page 3 of 15

4 (c) [10 POINTS] Assume that in May 2013, AA s commercial demand function/curve is what you calculated in part (b) and that AA s commercial capacity is of the unconstrained commercial revenue maximizing output. Calculate the optimal price and output in May 2013 for the case where optimal output is less than or equal to capacity. Use the appropriate constrained optimization method (there s no need to have the constraint that Show all calculations. Page 4 of 15

5 (d) [10 POINTS] What is the impact of a 1% excise tax on AA s commercial price, output, AA s revenues, tax revenues, and commercial customers welfare? State all assumptions and show all calculations. Page 5 of 15

6 (e) [10 POINTS] Should AA try to persuade the government not to tax AA s commercial price and to instead tax AA s commercial customers income? If so, explain your answer using a mathematical model and calculate the amount of the income tax; if not, explain your answer using a mathematical model and show why AA might be better off with an excise tax on its commercial price. State all assumptions and show all calculations. Page 6 of 15

7 (f) [5 POINTS] Assuming that all commercial customers can be modeled as a single representative consumer, derive the this representative consumer s utility function. State all assumptions and show all calculations. Page 7 of 15

8 Question 2 [35 POINTS] Consider an investor with a mean-variance utility function. (a) [5 POINTS] A risk free asset has no risk. Put another way, it offers a guaranteed return. That said, government bonds such as US 3 month T-Bills are often labeled risk free. However, as the following graph shows, the interest rate on US 3 month T-Bills (the return on the bonds ) have been anything but certain -- how do you explain this apparent contradiction? Page 8 of 15

9 (b) [5 POINTS] Why does finance model investors preferences over returns and risk by the mean-variance utility function? Page 9 of 15

10 (c) [5 POINTS] Suppose the investor has invested in a risky asset with expected return [ ] and risk. True or false: as the risky asset s risk rises, to remain indifferent to the initial return-risk bundle, the investor must be compensated with higher and higher compensating returns? Show all calculations. Page 10 of 15

11 (d) [10 POINTS] An investor with a mean-variance utility function allocates a fraction of her portfolio funds to a risky asset with expected return [ ] and variance and the remaining fraction ( to a risk free asset with return. All else equal, what happens to as the investor becomes less risk averse, the risk premium and the price of risk? Show all calculations. You must derive the expression for. Page 11 of 15

12 (e) [10 POINTS] In project 2 you were asked to synthesize three risky assets called let s say A, B and C. Write down the expression that was used to choose the weights of these three assets in the synthetic asset. Show all calculations. Let the expected returns of the three risky assets be [ ] [ ] [ ] and the risks of the three risky assets be. Do NOT solve for the weights and show all calculations. Page 12 of 15

13 Question 3 [20 POINTS] (a) [5 POINTS] Consider a production function with as inputs. True or false: if the production function exhibits increasing returns to scale then it must exhibit increasing returns to labor? Prove your answer by an example and show all calculations. Page 13 of 15

14 (b) [5 POINTS] Keystoned Corporation operates a pipeline carrying oil from Canada to the US. Keystoned wants to expand pipeline capacity and can do so by either doubling the size (radius) of the existing pipeline or build another identical pipeline. Assuming both options have the same cost should Keystoned double the current pipeline or build a new identical pipeline? What would happen to Keystoned s under your proposed option? Give a brief explanation. Page 14 of 15

15 (c) [10 POINTS] In June 2013, Jet-Airways purchased an aircraft for $200m with a useful life of 5 years. The opportunity cost rate of return for the first 3 years is 10% and the last two years 5%. Calculate the value of the aircraft and the price of using the aircraft in Jet-Airways operations in years and. Show all calculations and use the declining balance depreciation method. Page 15 of 15