CONSULTING PROJECT

Pricing and Production Decisions at PoolOut Ltd 

PoolOut Ltd manufactures and sells a single product called the "RainIn", which is a patent-protected automatic cleaning device for swimming pools. PoolOut's Rain In accounts for 72 percent of total industry sales of automatic pool cleaners. Its closest competitor, Pentair Pool Products, sells a competing pool cleaner that has captured about 18 percent of the market. Six other very small firms share the rest of the industry's sales. Using the last 26 months of production and cost data, PoolOut Ltd wishes to estimate its unit variable costs using the following quadratic specification: 

AVC= a0+a1Q + a2Q2

The monthly data on average variable cost (AVC), and the quantity of RainIn's produced and sold each month (Q) are presented in the table below.

PoolOut Ltd also wishes to use its sales data for the last 26 months to estimate demand for its RainIn. Demand for RainIn's is specified to be a linear function of its price (P), average income for households in the U.S. that have swimming pools (Mavg), and the price of the competing pool cleaner sold by Pentair Pool Products (PH): 
Qd = b0 + b1P + b2Mave + b3Ph 

The table below presents the last 26 months of data on the price charged for a RainIn (P), average income of households with pools (MAVG), and the price Pentair Pool Products charged for its pool cleaner (PH). I have created a Minitab Worksheet for you: PoolOut Ltd incurs total fixed costs of $45,000 per month. 

OBS AVC Q P MAVG PH Qsq

1 109 1647 275 58000 175 2712609
2 118 1664 275 58000 175 2768896
3 121 1295 300 58000 200 1677025
4 102 1331 300 56300 200 1771561
5 121 1413 300 56300 200 1996569
6 102 1378 300 56300 200 1898884
7 105 1371 300 57850 200 1879641
8 101 1312 300 57850 200 1721344
9 108 1301 325 57850 250 1692601
10 113 854 350 57600 250 729316
11 114 963 350 57600 250 927369
12 105 1238 325 57600 225 1532644
13 107 1076 325 58250 225 1157776
14 104 1092 325 58250 225 1192464
15 104 1222 325 58250 225 1493284
16 102 1308 325 58985 250 1710864
17 116 1259 325 58985 250 1585081
18 126 711 375 58985 250 505521
19 116 1118 350 59600 250 1249924
20 139 91 475 59600 375 8281
21 152 137 475 59600 375 18769
22 116 857 375 60800 250 734449
23 127 1003 350 60800 250 1006009
24 123 1328 320 60800 220 1763584
25 104 1376 320 62350 220 1893376
26 114 1219 320 62350 220 1485961

1. a. Run the appropriate regression to estimate the average variable cost function (AVC) for RainIn's. Evaluate the statistical significance of the three estimated parameters using a significance level of 5 percent. Be sure to comment on the algebraic signs of the three parameter estimates. 

1. b. Using the regression results from 1a, write the estimated total variable cost, average variable cost, and marginal cost functions (TVC, AVC, and MC) for PoolOut Ltd.

2. a. Run the appropriate regression to estimate the demand function for RainIn's. Evaluate the statistical significance of the three estimated slope parameters using a significance level of 5 percent. Discuss the appropriateness of the algebraic signs of each of the three slope parameter estimates.

2 b. The manager at PoolOut Ltd. believes Pentair Pool Products is going to price its automatic pool cleaner at $250, and average household income in the U.S. is expected to be $65,000. Using the regression results from 2a, write the estimated demand function, inverse demand function, and marginal revenue function.

3. Using your estimated cost and demand functions from parts 1 and 2, what price would you recommend the manager of PoolOut Ltd charge for its RainIn? Given your recommended price, estimate the number of units PoolOut Ltd can expect to sell, as well as its monthly total revenue, total cost, and profit. 
P: ___________ 
Q: ___________ 
TR: ___________ 
TC: ___________ 
Profit: ___________

4. For the profit-maximizing solution in question 3, compute the point elasticity of demand for RainIns. 

Ep = ______________ 

In the profit-maximizing situation in question 3, a 5 percent price cut would be predicted to _______________ (increase, decrease) quantity demanded of RainIns by ___________ percent, which would cause total revenue to _____________ (rise, fall, stay the same) and profit to _____________ (rise, fall, stay the same). 

5. For the profit-maximizing solution in question 3, compute the income elasticity of demand for RainIns. 

EM = ______________ 

a. Is the algebraic sign of the income elasticity as you expected? Explain. 

b. A 10 percent increase in Mavg would be predicted to _______________ (increase, decrease) quantity demanded of RainIns by ___________ percent. 

6. For the profit-maximizing solution in question 3, compute the cross-price elasticity of demand for RainIns. 

EXR = ______________ 

a. Is the algebraic sign of the income elasticity as you expected? Explain. 

b. A 3 percent decrease in PH would be predicted to _______________ (increase, decrease) quantity demanded of RainIns by ___________ percent. 

7. If total fixed costs increase from $45,000 to $55,000, what price would you now recommend in order to maximize profits at PoolOut Ltd? Compute the number of units sold at this price, total revenue, total cost and profit
P: ___________ 
Q: ___________ 
TR: ___________ 
TC: ___________ 
Profit: ___________ 

8. The other way we can estimate sales is with a forecasting technique. Estimate two models (of your choosing) to forecast estimated sales in period 27. Include measures of good fit and a 95% confidence interval around your forecast. Select one of the two models to present to your client.