eco204_summer_2009_HW_1

eco204_summer_2009_HW_1 - University of Toronto, Department...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain HW 1 Please help improve the course by sending me an email about typos or suggestions for improvements Question 1 In this question you will practice elasticities. Suppose a revenue maximizing airline currently charges $240 per seat and sells 100 seats per flight. If the airline cuts price to $235 and it expects to sell 100 seats. Should the airline cut prices? Answer by computing the price elasticity. Question 2 You are the proud owner of McCurryHurry, a fast food chain specializing in South Asian fast food cooking they give you the ingredients and tell you to go home and cook it yourself. The parent corporation "McCurryWeTakeYourMoneyinaHurry" has conducted market research across Canada and has found that the storelevel demand for McCurryHurry's best selling product, Chicken Brrr! Yani (it's Canada after all!) is: Q = 400 1,200 P + 0.8 A + 55 Pop + 800 Po Where Q = Sales of Chicken Brr! Yani per week, P = Price of Chicken Brr! Yani, A = advertising per week, Pop = Local population in thousands, Po = Price of other goods competing with McCurryHurry. Currently: P = $1.50, A = $1,000, Pop = 40, Po = $1. (a) How many Chicken Brr! Yani's can you expect sell per week? (b) Estimate the price elasticity for Chicken Brr! Yani. Any recommendations? (c) Estimate the advertising elasticity for Chicken Brr! Yani. (d) Derive the demand curve for your store 1 University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain Question 2 In this problem you will practice the concept of opportunity cost. Ajax SuperKomputers manufactures two products: electronic control devices (ECD) and specialty microchips. The microchips are a component of ECDs and can be sold to other high tech manufacturers for $550. The AC of microchips is $300 and the AC of ECDs is $500 plus the cost of two microchips. ECD sells for $1500. Currently, the microchips production facility is running at 100% capacity. (a) Suppose the company must either sell microchips or ECDs. Which one should it sell? (b) Suppose the company must either produce microchips or ECDs. Answer question (a) by posing the question as: "Should the company sell ECDs instead of microchips only?" Question 3 A company has the profit function: (Q) = 10 48Q + 15Q2 Q3 Suppose the company has a capacity of 7. Calculate the optimal output. Question 4 In this question you will practice the envelope theorem which gives us a simple technique for evaluating the change in the optimized objective when a parameter changes. Suppose a company estimates the demand and cost functions to be linear: P(Q) = a bQ C(Q) = TFC + c Q Where P is in $, Q is in `000s and a, b, TFC, c are positive parameters. (a) Interpret the parameters a, b, TFC, c. (b) Assuming there is no opportunity cost and unlimited capacity, derive an expression for the firm's profits with Q as the decision variable. (c) What is the optimal Q expressed as a function of the parameters a, b, TFC and c? (d) Use the envelope theorem to gauge the impact on the optimized profits from an increase of 1 unit from each the parameters a, b, TFC and c, holding all other parameters constant. (That is, what is the impact of raising the parameter a by 1 unit holding all other parameters constant). (e) Interpret the results in part (d). 2 University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain (f) If you, the manager had a budget to change one of the parameters (for the same cost) which one parameter would you pick and what would you do? (g) Optional Suppose you didn't know the envelope theorem. What is the impact on the optimized profits from an increase of 1 unit of the parameter a? (Of course, you should have the same answer as in part (d)). (h) Use the envelope theorem to gauge the impact on the optimized profits with price as the decision variable. Question 5 In this question you will do the airline question from the math handout. Ajax Airlines operates flights between London and Toronto. Ajax serves two types of consumers with demand functions: P1 = 330 - Q1 P2 = 250 - Q2 (a) Suppose all flights have a total of 180 seats capacity and must fly full. Solve for the revenue maximizing number of type 1 and type 2 passengers using the Lagrangian. (b) Will Ajax Air benefit from operating larger planes? 3 ...
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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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