# Estimating Demand Function

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 25

thclub. 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.

You have one week to complete the analysis, interpret the results, and summarize your findings and recommendations in a brief report. Sarah tells you that the main body of the report must be short (a 1000 words at most excluding the title page and any appendices), to the point, and not overly technical. She tells you that her formal knowledge of mathematics, economics, and statistics is somewhat limited, and asks you to keep that in mind as you write the main body of the report. Nevertheless, your conclusions and recommendations must be based on a rigorous analysis of the available data and you should provide a concise summary of any technical details

in an appendix. Sarah also tells you to be explicit about any important limitations your analysis might have. Finally, Sarah tells you that she likes her reports to be broken up into sections with sensible and self-explanatory headings because it makes them much easier to read and understand.

Sarah wishes you the best of luck and tells you to check with Peter, her personal assistant, about how to format the report. When you finally manage to track Peter down, he tells you to look at Section 0-8 of the MEQA Study Guide.

 Data for FitCo Clubs in 2008 Price (P) Demand (Q) Income (M) Population (N) Revenue Fixed cost Profit Town A \$62 2875 \$42,000 24000 \$178,250 \$101,000 \$77,250 Town B \$57 2908 \$35,000 30000 \$165,756 \$64,000 \$101,756 Town C \$84 3472 \$65,000 25000 \$291,648 \$137,000 \$154,648 Town D \$63 3263 \$45,000 28000 \$205,569 \$107,000 \$98,569 Town E \$60 2823 \$38,000 19000 \$169,380 \$77,000 \$92,380 Town F \$46 2502 \$26,000 22000 \$115,092 \$61,000 \$54,092 Town G \$64 2977 \$37,000 31000 \$190,528 \$68,000 \$122,528 Town H \$58 3309 \$41,000 28000 \$191,922 \$78,000 \$113,922 Town I \$63 2596 \$44,000 17000 \$163,548 \$70,000 \$93,548 Town J \$55 2517 \$29,000 26000 \$138,435 \$52,000 \$86,435 Town K \$83 3542 \$68,000 13000 \$293,986 \$166,000 \$127,986 Town L \$61 3132 \$50,000 12000 \$191,052 \$113,000 \$78,052 Town M \$52 2467 \$27,000 23000 \$128,284 \$32,000 \$96,284 Town N \$66 3881 \$51,000 32000 \$256,146 \$89,000 \$167,146 Town O \$60 2882 \$42,000 21000 \$172,920 \$66,000 \$106,920 Town P \$78 3629 \$56,000 37000 \$283,062 \$125,000 \$158,062 Town Q \$46 2931 \$32,000 15000 \$134,826 \$67,000 \$67,826 Town R \$55 2630 \$28,000 28000 \$144,650 \$40,000 \$104,650 Town S \$55 3381 \$41,000 18000 \$185,955 \$66,000 \$119,955 Town T \$30 4643 \$41,000 23000 \$139,290 \$84,000 \$55,290 Town U \$41 4945 \$56,000 26000 \$202,745 \$114,000 \$88,745 Town V \$28 4784 \$37,000 32000 \$133,952 \$56,000 \$77,952 Town W \$22 3311 \$24,000 24000 \$72,842 \$36,000 \$36,842 Town X \$43 4066 \$42,000 18000 \$174,838 \$96,000 \$78,838