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# COST STRCTURE and PRICING: Sting Ray

COST STRCTURE and PRICING: Sting Ray
PoolVac, Inc. manufactures and sells a single product called the "Sting Ray," which is a patent-protected automatic cleaning device for swimming pools. PoolVac's Sting Ray faces its closest competitor, Howard Industries, also selling a competing pool cleaner. Using the last 26 quarters of production and cost data, PoolVac wishes to estimate its average variable costs using the following quadratic specification:
AVC = a + bQ + cQ 2(Squared)
The quarterly data on average variable cost (AVC), and the quantity of Sting Rays produced and sold each quarter (Q) are presented in the data file. PoolVac also wishes to use its sales data for the last 26 quarters to estimate demand for its Sting Ray. Demand for Sting Rays is specified to be a linear function as the following:
Qd = d + eP + fM + gPH
in which its price (P), average income for households in the U.S. that have swimming pools (M), and the price of the competing pool cleaner sold by Howard Industries (PH).

QUESTIONS

1. Run the appropriate regression to estimate the average variable cost function (AVC) for Sting Rays. 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.

2. Given your answer in 1, show the estimated total variable cost, average variable cost, and marginal cost functions (TVC, AVC, and MC) for PoolVac.

3. Apply dummy variable to construct the time-series quarterly sales estimation of Sting Ray (Hint: Q = A+Bt+...). Please predict the quantity sold in the first quarter 2013.

4. Run the appropriate regression to estimate the demand function for Sting Rays.
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.

5. The manager at PoolVac, Inc. believes Howard Industries 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 Question 4, write the estimated demand function (with only P as the independent variable), inverse demand function, and marginal revenue (MR) function.

6. Given your MC function in question 2 and MR function in question 5, what is the profit-maximizing unit price PoolVac should charge for Sting Ray?

#### Solution Preview

See the attached file. Thanks

Sting Ray-PoolVac, Inc.
Quarter/Year Period (t) AVC Q Q^2 P M PH
1st/2006 1 109 1647 2712609 275 58000 175
2nd/2006 2 118 1664 2768896 275 58000 175
3rd/2006 3 121 1295 1677025 300 58000 200
4th/2006 4 102 1331 1771561 300 56300 200
1st/2007 5 121 1413 1996569 300 56300 200
2nd/2007 6 102 1378 1898884 300 56300 200
3rd/2007 7 105 1371 1879641 300 57850 200
4th/2007 8 101 1312 1721344 300 57850 200
1st/2008 9 108 1301 1692601 325 57850 250
2nd/2008 10 113 854 729316 350 57600 250
3rd/2008 11 114 963 927369 350 57600 250
4th/2008 12 105 1238 1532644 325 57600 225
1st/2009 13 107 1076 1157776 325 58250 225
2nd/2009 14 104 1092 1192464 325 58250 225
3rd/2009 15 104 1222 1493284 325 58250 225
4th/2009 16 102 1308 1710864 325 58985 250
1st/2010 17 116 1259 1585081 325 58985 250
2nd/2010 18 126 711 505521 375 58985 250
3rd/2010 19 116 1118 1249924 350 59600 250
4th/2010 20 139 91 8281 475 59600 375
1st/2011 21 152 137 18769 475 59600 375
2nd/2011 22 116 857 734449 375 60800 250
3rd/2011 23 127 1003 1006009 350 60800 250
4th/2011 24 123 1328 1763584 320 60800 220
1st/2012 25 104 1376 1893376 320 62350 220
2nd/2012 26 114 1219 1485961 320 62350 220

COST STRCTURE and PRICING: Sting Ray
PoolVac, Inc. manufactures and sells a single product called the "Sting Ray," which is a patent-protected automatic cleaning device for swimming pools. PoolVac's Sting Ray faces its closest competitor, Howard Industries, also selling a competing pool cleaner. Using the last 26 quarters of production and cost data, PoolVac wishes to estimate its average variable costs using the following quadratic specification:
AVC = a + bQ + cQ^2
The quarterly data on average variable cost (AVC), and the quantity of Sting Rays produced and sold each quarter (Q) are presented in the data file. PoolVac also wishes to use its sales data for the last 26 quarters to estimate demand for its Sting Ray. Demand for Sting Rays is specified to be a linear function as the following:
Qd = d + eP + fM + gPH
in which its price (P), average income for households in the U.S. that have swimming pools (M), and the price of the competing pool cleaner sold by Howard Industries (PH).
QUESTIONS
1. Run the appropriate ...

#### Solution Summary

This post explains how to built a demand examination

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