Data for FitCo Clubs in 2008 Smart Health develops private fitness clubs in smal

Question

Data for FitCo Clubs in 2008

Smart Health develops private fitness clubs in small towns. Smart Health 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 . Smart Health 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 Smart Health has opened 24 such clubs in different towns.

You have just started working for Smart Health, and your new boss, Karen, gives you a copy of an Excel spreadsheet containing data collected last year on Smart Health’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. Smart Health 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.

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 25000 $        138,435 $    52,000 $    86,435 Town K $              83 3542 $        68,000 14000 $        293,986 $ 166,000 $ 127,986 Town L $              61 3132 $        50,000 12000 $        191,052 $ 113,000 $    78,052 Town M $              52 2467 $        28,000 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 29000 $        144,650 $    40,000 $ 104,650 Town S $              55 3381 $        41,000 19000 $        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 33000 $        133,952 $    56,000 $    77,952 Town W $              22 3311 $        24,000 25000 $          72,842 $    36,000 $    36,842 Town X $              43 4066 $        42,000 18000 $        174,838 $    96,000 $    78,838

Explanation / Answer

1) Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3159.183 255.6624 12.35686 6.42E-10 2619.783 3698.583 2619.783 3698.583 Price -67.1161 4.742406 -14.1523 7.76E-11 -77.1217 -57.1105 -77.1217 -57.1105 Imcome 0.032886 0.011341 2.899831 0.009966 0.008959 0.056812 0.008959 0.056812 Population 0.012857 0.006495 1.979372 0.064203 -0.00085 0.026561 -0.00085 0.026561 DEMAND(Q) = 3159.183-67.1161P+0.03M+0.058N 2) the demand is positively affected by income and population. Higher the income and higher the population more is the demand. However, a negative relationship exists between demand Q and Price P 3)elasticity = (dQ/dP)*(P/Q) dQ/dP = -67.12 P/Q for town D = 3263/63 P/Q = 51.79 elasticity = -67.12*51.79 elasticity in town D = 3,476.389 4) PROFIT IS MAXIMIZED AT P = $66 Town H charges P= $58

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