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ECON 3305 Dr. Chen CASE 2 - COST STRCTURE and PRICING: Sting

Dear Tutor team, Please help me on my assignment. Please use your own words. Please show formula on Excel also. Please so not share my assignment or answer for the other.  Thanks!

ECON 3305 Dr. Chen




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 variables to construct the time-series quarterly sales estimation of


Sting Ray (Hint: Q = A+Bt+D1t?). Please predict the quantity sold in the first quarter


2014. (10%)


4. Run the log-linear regression to estimate the demand function for Sting Rays.


Evaluate the statistical significance of the three estimated coefficients of parameters


by using a significance level of 5 percent. Discuss the elasticities (price elasticity of


demand, income elasticity and cross-price elasticity) to define the characters of Sting


Ray. (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. Please run a multiple linear regression then explore the


inverse demand function (i.e. Price is dependent variable) and marginal revenue


(MR) function (Hint: Half-way rule). (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? (Hint: Solve the


quadratic equation by quadratic formula (10%)






? b ± b 2 ? 4ac






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