<p>Fall 2013 AGEC 317 Capps</p><p>Problem Set #2</p><p>1 1 1. Verify the demand function. Q  p b , where a > 0, b> 0, has constant demand a elasticity. a) Verify the own-price elasticity of demand does not depend upon Q and p.</p><p> b) The parameters a and b of the demand function are restricted to be positive. Why?</p><p>2. Management of McPablo’s Food Shops has completed a study of weekly demand for its “old-fashioned” tacos in 53 regional markets. The study revealed that </p><p>Q  400 1,200P  0.8A  55Pop  800P 0 ,</p><p> where Q is the number of tacos sold per store per week, A is the level of local advertising expenditures (in dollars), Pop denotes the local population (in thousands), and P0 is the average taco price of local competitors. For the typical McPablo’s outlet, P = $1.50, A = $1,000, Pop = 40, and P0 = $1.</p><p> a) Estimate the weekly sales for the typical McPablo’s outlet?</p><p> b) What is the own-price elasticity for tacos? What is the advertising elasticity? </p><p> c) Should McPablo’s raise its taco price? Why or why not?</p><p>Capps 1 3. Suppose that the demand and supply curves for a particular commodity are given as follows:</p><p>Qd = 80,000 – 4,000P, and Qs = -18,000 + 10,000P.</p><p>Qd refers to the quantity demanded, Qs= refers to the quantity supplied, and P corresponds to the price.</p><p> a) Find the market equilibrium price (P) and quantity (Q).</p><p> b) What is the elasticity of demand and supply at the equilibrium price?</p><p> c) When P = $6, does a surplus or shortage exist?</p><p> d) What is the magnitude of the surplus or shortage?</p><p>Capps 2 4. Suppose that Atlantis, Inc., the manufacturer of a microcomputer chip faces demand and cost equations given by Q = 8.5 - 0.05P and TC = 100 + 38Q. Q corresponds to the number of lots of computer chips produced and P corresponds to the price per lot.</p><p> a) Derive the inverse demand function.</p><p> b) Derive the revenue function. Express your answer in terms of Q.</p><p> c) Derive the profit function. Express your answer in terms of Q.</p><p> d) What value of Q maximizes profit for Atlantis, Inc? Provide both first-order and second-order conditions to substantiate your answer.</p><p> e) What price should Atlantis, Inc. charge for a particular lot of computer chips to assure profit maximization?</p><p> f) What is the maximum level of profit Atlantis, Inc. may earn?</p><p>Capps 3 5. Suppose that you gain employment with Chili’s Restaurants as a research analyst. You note that historically Chili’s sells 20,000 fajita entrees among various locations in the Dallas Metroplex when the price per entrée is $10.00. You also realize that the own-price elasticity for fajita entrees is -1.5.</p><p> a) Is this own-price elasticity a reasonable estimate of behavior of Chili’s patrons? Why or why not?</p><p> b) Suppose that management wishes to lower the price of fajita entrees to $9.00. Provide a prediction of the number of fajita entrees that will be sold at this price. Show all work.</p><p> c) Will this action, all other factors invariant, result in a rise or fall in sales revenue?</p><p> d) What is the magnitude of the gain or loss in revenue?</p><p>Capps 4 6. The demand for Kellogg’s Raisin Bran cereal is given as:</p><p>1.4 0.75 0.65 0.12 0.05 QKRB = 0.25PKRB PGMC PKFF I A , where</p><p>QKRB denotes the quantity of Kellogg’s Raisin Bran sold, PKRB denotes the price of Kellogg’s</p><p>Raisin Bran, PGMC denotes the price of General Mills Cheerios, PKFF represents the price of Kellogg’s Frosted Flakes, I represents U.S. disposable income, and A represents the level of advertising expenditures associated with Kellogg’s Raisin Bran.</p><p> a) What is the technical name of this type of demand function?</p><p> b) TRUE or FALSE. The demand for Kellogg’s Raisin Bran is elastic. </p><p> c) If General Mills raises the price of Cheerios by 4 percent, then the quantity of Kellogg’s Raisin Bran sold rises by ______percent, all other factors invariant. Show all work.</p><p> d) Both General Mills Cheerios and Kellogg’s Frosted Flakes are ______for Kellogg’s Raisin Bran.</p><p> e) True or False. The chief competitor of Kellogg’s Raisin Bran is Kellogg’s Frosted Flakes. Shed light on your answer.</p><p> f) To offset a 5 percent increase in the price of Kellogg’s Raisin Bran, by how much should Kellogg increase their advertising expenditures associated with this cereal? Show all work.</p><p>Capps 5 g) What type of good is Kellogg’s Raisin Bran cereal? Shed light on your answer.</p><p> h) List two additional factors, besides those that have been given, that would potentially affect the demand for Kellogg’s Raisin Bran.</p><p>7. Hirschey, P3.10 (pp 106-107)</p><p>Capps 6 </p>