Unformatted text preview: University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain HW 9 Please help improve the course by sending me an email about typos or suggestions for improvements Question 1 Note: There are two parts (A and B) to this question. Part A appeared as a practice problem in 2008 2009 while part B appeared as a Test question in 2008 2009. See if you can handle the transition from a practice problem to a test question. Part A Ajax Air (AA) is the exclusive carrier on the Toronto Niagara Falls route. AA needs to determine the number of flights per week and the fare per passenger. After totaling operating and fuel costs, airport charges, sobering up pilots etc. it calculates the operating cost per flight to be $4,000. Each aircraft carries 100 passengers and the airline expects to fly all flights filled to capacity (i.e. there is ample demand for travel to ensure that all seats will be sold). AA estimates weekly demand to be P = 120 0.1Q where Q is number of passengers and P is the fare in dollars. For this question, assume that MC is AVC. 1 ( This is a footnote). (a) What is the MC of each passenger? 1 Technically MC AVC: to see what MC really is, consider a flight. If no seats are sold, then assume that the flight does not take off (in real life, this is not true because a flight may have to pick up passengers from the destination and travel to another city thus even if there are no passengers at the origin city, the flight must depart. When the first seat is sold, the flight must take off. The MC of the first passenger is $4,000 (the full operating cost of the flight). Given that with a single booking the flight must depart, the MC of the second, third etc. passengers are all zero. 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (b) What is the optimal number of flights per week and the passenger fare? (c) Take your answer in part (b) as the AA's capacity. Suppose AA has been offered $6,000 per week to carry freight. Assume that a freight flight does not carry passengers and vice versa. How many passenger and freight flights should AA operate? Assume AA does not have fixed costs. What is the passenger fare? Hint: use the opportunity cost technique. (d) Solve part (c) as a "multivariate" decision problem. Don't forget the constraint that QP + QF = 400 where the subscript "P" is for passengers and "F" is for freight. PART B Ajax Air (AA) is the exclusive carrier on the Toronto Niagara Falls route. AA needs to determine the number of flights per week and the fare per passenger. After totaling operating and fuel costs, airport charges, sobering up pilots etc. it calculates the operating cost per flight to be $4,000. Each aircraft carries 100 passengers and the airline expects to fly all flights filled to capacity (i.e. there is ample demand for travel to ensure that all seats will be sold). AA estimates weekly demand to be P = 120 0.1Q where Q is number of passengers and P is the fare in dollars. For this question, assume the MC is AVC. 2 ( This is a footnote) (a) What is the MC of each passenger? (b) What is the optimal number of flights per week and the passenger fare? (c) Take your answer in part (b) as the AA's capacity. Suppose AA has been offered a deal to carry freight. Assume that a freight flight does not carry passengers and vice versa. What is the offer to carry freight (price per plane?) if Ajax chooses to allocate 50% of the fleet to passenger flights and 50% to freight flights? Assume AA does not have fixed costs. What is the passenger fare with the option to carry freight? 2 Technically MC AVC: to see what MC really is, consider a flight. If no seats are sold, then assume that the flight does not take off (in real life, this is not true because a flight may have to pick up passengers from the destination and travel to another city thus even if there are no passengers at the origin city, the flight must depart. When the first seat is sold, the flight must take off. The MC of the first passenger is $4,000 (the full operating cost of the flight). Given that with a single booking the flight must depart, the MC of the second, third etc. passengers are all zero. 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Question 2 (20082009 Test Question) Brieoni makes hand tailored suits for men. It owns the entire supply chain from manufacturing and distribution to retailing. Brieoni's cost function is C = 1,000,000 + 20,000Q where Q is the number of suits and C is in dollars. 75% of Brieoni's MC is due to manufacturing, 12.5% due to distribution and 12.5% due to retailing. For the planning period April 2009, Brieoni's managers estimate demand to be: P = 66,000 0.1Q where Q is number of suits and P is in dollars. You are in charge of output and pricing decisions at Brieoni. Your compensation is linked to Brieoni's P/L (profit/loss). (a) How many suits will you manufacture in April 2009? At what price? Show your calculations. (b) Brieoni's accountants have to report financial figures to investors. They ask you for the April 2009 gross margin to revenue ratio. What is it? Show your calculations. (c) Brieoni's marketing department is preparing a marketing plan for April 2009. They want to know the potential impact on quantity due to a 10% decrease in price. Use your answer in part (b) to respond to the marketing department's request. Show your calculations. (d) Suppose, after manufacturing but before distributing the quantity of suits in part (a), demand estimate for Brieoni's suits is revised to P = 46,000 0.1Q. At the same time, the manufacturing facility's fixed cost increases by $500,000. How will this impact Brieoni's price and quantity from part (a)? Show your calculations and explain your answer. (e) Return to facts in part (d): suppose, after manufacturing but before distributing the quantity of suits in part (a), the estimate for demand for Brieoni's suits is revised to P = 46,000 0.1Q and the manufacturing facility's fixed cost increases by $500,000. At the same time (as is typical in the outlets business) another company "Sucks Fifth Avenue" offers Brieoni $5,000 per suit for an unlimited number of suits. Based on your answer in part (a), how should you respond to "Sucks Fifth Avenue" offer? Show your calculations and explain your answer. Do not solve this problem as a multivariate problem. (f) Solve part (e) using a multivariate approach. For your convenience, here is the question again: Return to facts in part (d): suppose, after manufacturing but before distributing the quantity of suits in part (a), the estimate for demand for Brieoni's suits is revised to P = 46,000 0.1Q and the manufacturing facility's fixed cost increases by $500,000. At the same time as is typical in the outlets business another company "Sucks Fifth Avenue" offers Brieoni $5,000 per suit for an unlimited number of suits. Based on your answer in part (a), how should you 3 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain respond to "Sucks Fifth Avenue" offer? Show your calculations and explain your answer. Solve this problem as a multivariate problem. Question 3 (20082009 Test Question) Burger Queen (BQ) sells the "Slopper" (a burger made of mystery meat) through independently owned franchise restaurants. BQ sells ingredients for the Slopper at cost to franchise restaurants. Suppose the MC of ingredients is $1. Under the terms of the current contract, BQ takes 25% of every franchise's revenues and BQ sets the price. (a) Daily demand for a franchise in North York with a daily capacity of 600 sloppers is estimated to be P = 6 Q/200. Calculate the optimal price and daily sales of sloppers for this location. Show all calculations. (b) Suppose the BQ shares a percentage of total profits with the North York franchise. Calculate the optimal price and daily sales of sloppers. Show all calculations. (c) Daily demand for a franchise in Mississauga with a capacity of 500 sloppers/day is estimated to be P = 6 Q/200. Calculate the optimal price and daily sales of sloppers for this location under the contract where BQ takes 25% of the franchisee's revenues. Show all calculations. Question 4 (20082009 Final Exam Question) Lb. Cake Corporation is a cake franchisor. Under the terms of the current contract with a restaurant on the U Toronto campus, Lb. Cake takes a fraction of the restaurant's revenues (R) and incurs a fraction of the restaurant's total cost (C). Lb. Cake supplies ingredients to the restaurant with a markup over AC: assume AC is constant and the restaurant has no other costs besides the cost of ingredients. Suppose the restaurant has a capacity of 700 cakes a day. Daily demand is given by the equation: P = 100 10 Q P is in dollars per cake and Q is in hundreds of cakes. Suppose = 0.2, = 0.25, AC = $8 per hundred cakes, and, Lb. Cake charges a 100% markup over AC. (a) If Lb. Cake chooses the price and quantity at the UT location, solve for the optimal P and Q. Show all calculations. 4 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (b) Lb. Cake has an opportunity to renegotiate the contract: it can change either or by 0.1 or the markup by 10%. Lb. Cake approaches you for advice on which parameter to change. What is your advice? Show all calculations. Question 5 Suppose a Canadian company has the demand equation: Q = 3P2 A3 Y4 Where A is advertising and Y is income. (a) What are the price, advertising and income elasticities? Interpret these. (b) If the company has MC = $10 what is the profit maximizing price? (c) Suppose the Canadian company exports to China. The cost of shipping, tariffs to China raises the MC to $15 (i.e. MCChina = $15). How price sensitive must the Chinese market be for the Chinese price to be lower than the Canadian price? 5 ...
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 Economics, Microeconomics, S. Ajaz Hussain

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