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 + cQ2, (0.1)

The quarterly data on average

variable cost (AV C), 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, (0.2) 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).

Sting Ray- PoolVac , Inc.

Quarter/YearPeriod (t)AVCQPMPH

1st/20061109214723258000132

2nd/20062118216423258000132

3rd/20063121179531358000213

4th/20064102183131356300213

1st/20075121191331356300213

2nd/ 20076102187831356300213

3rd/20077105187131357850213

4th/20078101181231357850213

1st/20089108180132657850250

2nd/200810113135436057600260

3rd/200811114146336057600260

4th/200812105173832657600226

1st/200913107157632658250226

2nd/200914104159232658250226

3rd/200915104172232658250226

4th/200916102180832658985260

1st/201017116175932658985260

2nd/201018126121137358985260

3rd/201019116161836059600260

4th/20102013959148259600382

1st/20112115263748259600382

2nd/201122116135737360800260

3rd/201123127150336060800260

4th/201124123182833060800230

1st/201225104187633062350230

2nd/201226114171933062350230

1.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. (20%)