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You have just started work for a small company, FitCo, that develops private fitness clubs in small towns. FitCo buys or leases a local hotel or motel, then renovates to provide a gym, swimming pool, sauna, Jacuzzi, and a small café where patrons can buy juices, smoothies, and other healthy snacks . FitCo only develops clubs in towns where it has no competitors. The main product is a one-month membership, which gives patrons unlimited use of the gym and other club facilities. So far FitCo has opened 24 such clubs in different towns.
Your new boss, Sarah, gives you a copy of an Excel spreadsheet containing data collected last year on FitCo’s 24 existing clubs. She asks you to use the data to complete the following important and time-sensitive tasks:
1. Estimate an empirical demand function for one-month memberships using the data gathered from the firm’s 24 clubs. (Assume the demand function is linear. Further assume that the only variables likely to significantly affect the demand for one-month memberships are price, average income, and the size of the town’s population.)
2. Interpret the estimated demand function for one-month memberships.
3. Calculate the point price elasticity of demand and point income elasticity of demand in Town D at the price charged last year.
4. For Town H and Town W determine whether the price charged last year was above, below or equal to the profit-maximizing price.
5. FitCo is considering opening a 25th club. The company must choose between one of two towns in which to locate the new club. Both towns have populations of 22,000. However, one of the towns has a relatively high average income of \$60,000, while the other has a relatively low average income of \$45,000. The annual fixed costs of running the club in the high income town would be about \$160,000, while annual fixed costs of running the club in the low income town would be about \$70,000. Your job is to select the site for the 25th club and to determine the appropriate price for the one-month memberships.
6. Write a short report summarizing the results of the analysis and any recommendations.