# You are a manager in a large hotel chain that is about

2. You are a manager in a large hotel chain that is about to open a hotel in a new city. You have been asked to determine the nightly rates that should be charged to the two distinct groupsof customers that will stay at this hotel: tourists and business travelers. You can separate (and so identify) members of each group based on advanced booking. Therefore, you plan toimplement third-degree price discrimination. To help you determine the profit-maximizing price for each group, you use a sample of data you have on these same groups customers forhotels the chain operates in 50 other cities (these data can be found below). Based on prior research, you know that demand for both groups exhibit constant elasticity. Therefore, inusing the data below, you will assume an exponential demand function, of the form: Q = AP n, where Q is output (number of nightly stays per month), P is price (per night), A is a constant,and ",n", is the (constant) price elasticity of demand. Part I: For each group of customers, run an Excel regression to estimate ",n,", the price elasticity of demand for that group. NOTE: Since this is an exponential function, you will have to first transform the data into natural logs in order to estimate a linear regression of the form: LN(Q) = b1LN(A) + nLN(P). In this form, the estimated coefficient for the log of P (i. e. ",n",) will be, in fact, your estimate of the price elasticity of demand for that group. ALSO, because ",n", is the price elasticity ofdemand, you should obtain a negative value from your regression and not omit the minus sign as you do your calculations. Part II: Use the results of your regressions to answer the question (determining the profit-maximizing price for each group). a. Based on your regression results, enter a formula in the respective boxes below to calculate the profit-maximizing price for each group of customers. NOTE: Assume marginal cost for each nightly stay is $50. Round your answers to the nearest dollar. Tourists: Business Travelers: DATA: TouristsPrice (per night)195208165184192198182193143156194143194163198154210150197195175177159146150207182148144157148194167194185142172140187202209180Nightly Stays per Month(000s)363051433937444058554159374640563551403940405060553142595853563947393756416441333144Business TravelersPrice (per night)232222274300263292227294284291296226240259291237243237258293266221254260236239254230260228233298265221298255257237230225279253Nightly Stays per Month(000s)283021212219262223221927252222282727252222292324262623262327281822271925222827292326202194149199174206181171323456344138444225024924525022929028328526232625292021213. You have just become the manager of a private golf club, and have been asked to come up with an annual membership (entry) fee as well as a price to charge for each round (18 holes)of golf. You have previously managed public golf courses and know from experience there are two types of golfers: ",serious", and ",occasional. ", In fact, you have annual survey data fromyour previous job in which you collected (for four years) data on the number of rounds each golfer played that year as well as whether the golfer had a subscription to the publication,",Golfer’s Digest. ", A sample of the data can be found at the bottom of this problem, in which you divided it into two groups of golfers: 100 observations of ",serious", golfers (those with asubscription to ",Golfer’s Digest",) and 100 observations of ",occasional", golfers (those without a subscription). Along with the annual number of rounds for each golfer, you also have theprice of a round of golf corresponding to the year when the round was played. Part I: For each group of 100 golfers, run an Excel regression to estimate a simple demand equation (i. e. Q = a – bP), where Q represents the number of rounds of golf , P is the price perround, and ",a", and ",b", are the parameters to be estimated by the regression. Part II: Use the results of your regressions to answer the questions below. NOTE: Assume, for all questions, that the club incurs a marginal cost of $10 for each round of golf. a. Based on your regression results, write the general expression for the respective demand equationNOTE: Round constant term to nearest whole number and slope coefficient to two decimal places (e. g. Q = 56 – 1. 34P). Serious Golfer Demand: Occasional GolferDemand: Serious Golfers Only: Suppose you want to consider what the club’s profit would be if you limited membership to ",serious", golfers. b. How much would the club charge for each round of golf?c. Enter a formula to calculate the annual membership (entry) fee charged to each golfer. d. Based on just the number of golfers in this sample of data, enter a formula to calculate the club’s profit?NOTE: For purposes of this question, assume there are no fixed costs. Both Types of Golfers: Now consider what the club’s profit would be if you priced such that you could attract both groups of golfers. e. How much would the club charge for each round of golf?NOTE: Round answer to the nearest dollar. f. Enter a formula to calculate the annual membership (entry) fee charged to each golfer. g. Based on just the number of golfers in this sample of data, enter a formula to calculate the club’s profit?NOTE: Again, assume there are no fixed costs. DATA: Serious GolfersOccasional GolfersAnnual Rounds(18 holes)Annual Rounds(18 holes)Price5957545958545759605658585456576055575858545656515151575251555757555456555851525657585353575654585853555350524951555051514953555151515348505451514820. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0026. 0026. 00Price2121202323232220222021222222212220221922212122201922202220192221212219192020222018182121202120211821192119191820212018202121212021202021192020181920. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0020. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0022. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0024. 0026. 0026. 0026. 0046474848474750475251455045515248454646475147514851455026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0017202020201917201818201919201917171717201719181819201926. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 0026. 004. An aerospace company has two divisions. The first division makes rockets, purchased by both the government and private firms. The other division makes the engines used by thoserockets. (NOTE: Each rocket requires one engine). Marginal cost in the engine division is a constant $7. 92 million, while marginal cost in the rocket division–excluding the cost of theengine–is a constant $16 million (thus, in this problem, AVC = MC). In addition, the price elasticity of demand for rockets (by all purchasers) is a constant -1. 62 at every price level, withdemand for rockets given by the function: Q = 36,520P –1. 62. For this entire problem, assume pricing is conducted over the long run (AC = AVC: all costs are variable). In answering the questions below, you will consider two scenarios: Part I: No external market for engines (they are strictly inputs to the company’s rocket division). Part II: Engines have their own external market, which is given by the inverse demand function: P = 22 – 0. 15Q, where P is the price (in millions) and Q is the quantity of engines. NOTE: Use marginal-cost pricing (MR=MC) to determine the engine division’s profit-maximizing quantity and price (when there is an external market), but always use cost-plus pricing todetermine the price of a rocket. Part I (No External Market for Engines): a. What is the profit-maximizing price of a rocket (in millions of dollars)?NOTE: Round your answer to two decimal places. b. Enter the formula to calculate the profit-maximizing quantity of rockets. c. What is the company’s profit (rocket and engine divisions combined), in millions?Part II (External Market for Engines Exists): a. What is the profit-maximizing quantity and price (in millions) of engines?NOTE: Enter formulas in the respective boxes below. Round both to nearest whole number. Equilibrium Quantity: Equilibrium Price: b. Enter a formula to calculate the profit (in millions) of the engine division. c. Calculate the profit-maximizing price and quantity of rockets. NOTE: Round both to nearest whole number. Equilibrium Price: Equilibrium Quantity: d. What is the company’s overall profit (both divisions combined)–in millions?e. Is the company buying or selling engines on the open market? Briefly explain.