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).
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. (30%)
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. (15%)
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. (10%)
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. (20%)
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. (15%)
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? (10%)
Sting Ray-PoolVac, Inc.
Quarter/Year Period (t) AVC Q P M PH
1st/2006 1 109 1647 275 58000 175
2nd/2006 2 118 1664 275 58000 175
3rd/2006 3 121 1295 300 58000 200
4th/2006 4 102 1331 300 56300 200
1st/2007 5 121 1413 300 56300 200
2nd/2007 6 102 1378 300 56300 200
3rd/2007 7 105 1371 300 57850 200
4th/2007 8 101 1312 300 57850 200
1st/2008 9 108 1301 325 57850 250
2nd/2008 10 113 854 350 57600 250
3rd/2008 11 114 963 350 57600 250
4th/2008 12 105 1238 325 57600 225
1st/2009 13 107 1076 325 58250 225
2nd/2009 14 104 1092 325 58250 225
3rd/2009 15 104 1222 325 58250 225
4th/2009 16 102 1308 325 58985 250
1st/2010 17 116 1259 325 58985 250
2nd/2010 18 126 711 375 58985 250
3rd/2010 19 116 1118 350 59600 250
4th/2010 20 139 91 475 59600 375
1st/2011 21 152 137 475 59600 375
2nd/2011 22 116 857 375 60800 250
3rd/2011 23 127 1003 350 60800 250
4th/2011 24 123 1328 320 60800 220
1st/2012 25 104 1376 320 62350 220
2nd/2012 26 114 1219 320 62350 220
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Sobharani Yerra YerraSobharani Yerra Yerra answered this 4 minutes later
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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. Answer?Use the excel to this regression analysis:
AVC?? Coefficients t Stat P-value
Intercept 152.8806 6.605126 23.14575 1.95807E-17
Q -0.06141 0.014622 -4.19949 0.000342469
Q2 2.18E-05 8.1E-06 2.692745 0.0129909
Because the P values of all 3 variables are below the 5% confidence interval, each variable should be considered statistically significant. a>0,b<0,c>0, it meet the theory. The mathematical operators indicate a trend that conforms with the AVC curve: That is, the trend first goes down and then increases again
CommentSobharani Yerra YerraSobharani Yerra Yerra answered this 25 minutes later
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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. (15%)
TVC = 152.8806 Q - 0.06141Q^2 +0.00002181 Q^3
AVC = 152.8806 - 0.06141Q+0.00002181 Q^2
MC = 152.8806 - 0.06141Q+0.00006543 Q^2
hen AVC is minimum, the MC =0. So Qmin = -b/2c=1407.6, AVCmin =109.6
Comment : I do not understand number 2 of the BOLD part, can some one explain.
Can someone Answer questions 3 , question 4, question 5, and question 6 . Please.
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